International development worker - “a bit like a missionary and a charity worker, but without the God part”.
Translator, writer and editor is fairly easy to explain, but not the fact that all my work is done on a laptop and received and sent via e-mail.
I’m a lawyer, which is easy enough to explain.
I think it would be hard for them to understand my area of focus, which is juvenile delinquency and child abuse cases. Childhood and adolescence (which I don’t even think was conceptualized back then) are so different now that I think it would be almost impossible to explain exactly what it is that I do to someone who doesn’t have an idea of what modern childhood is like.
I’m trying to save the trees you are cutting down to make your house…Errr…Ummm…Keep up the good work with your oxen and mules, don’t switch to something coming down the road called gasoline, it’ll turn your blood black and make you think weird thoughts about your infidel brethren across the great sea.
Oh and back off killing those whales, the oil is over rated and makes your house stink - get that windmill up for the time being 
Phlosphr - E.D. of large environmental advocacy group in New England.
My job is so abstract that no friends or family including my wife really know what I do. I work for a mega-corp that does outsourcing for benefits administration for some of the biggest companies in the U.S. Clients contract with us to build call centers and maintain their employee information to shoot it out to various insurance carries and other types of vendors. I work in the back-end and I do programming for the hardest problems but I also co-manage a group in India consisting of about 40 employees who do the more basic programming. We maintain at least two databases per client and build custom files based on specifications and the vendor. We also have to be experts on U.S. benefits laws like COBRA and FMLA among others.
Somehow I think that is too many concepts for our friend in question to process.
This may take some time, so go make a pot of coffee.
First, you know how you can see things in the dark when you’re wandering around your house carrying a candle? That’s because the candle is throwing off light, and that light is bouncing off of things, and it comes back into your eyes, which is how you can see them. Keep that in the back of your mind.
Well, there are these two guys – Nikola Tesla and Guglielmo Marconi, currently (~1893-1900) arguing about who invented this device called a ‘radio’ that sends peoples’ voices through the air so other people can hear them. What’s really going on is that the radio transmitter is throwing off a kind of light that you can’t see. No, really. It’s just like light, but you can’t see it.
So, some other guys figured out how to use radios to do the same thing that your candle does – the radio waves go out, bounce off of things, and come back, and we’ve got an impossibly complicated machine that can read the waves coming back and tell us if something is out there, and some other things like how fast it’s going, what direction it’s pointed in, and some other stuff. It’s called a radar.
Now, there’s this whole branch of mathematics based around what we call “Imaginary Numbers.” They’re just like regular numbers, only imaginary. If we pretend that we believe in these imaginary numbers, we can work out all sorts of complicated equations that solve problems in imaginary space. No, I’m not going to explain it any more – this stuff has been around since the first century, so it should be old news to you. Anyway, when the radar looks out at things, all that it sees is a big mass of garbled data. If we pretend that all this data is really in imaginary space, and solve a bunch of equations in imaginary space, then we convert the answers back to real space, the radar can suddenly see things more clearly. The cool thing: it’s all imaginary. I don’t even believe this stuff, but the answers actually work AND THEY PAY ME MONEY FOR IT!
Okay, now there’s this guy named Hollerith who developed this “tabulating machine” to help with the 1890 census. That tabulating machine, which basically just adds numbers, is really important. We have what in effect are infinitely large tabulating machines that control EVERYTHING, including these radars. I work on the designs of these machines to get the radars to do useful things.
Now, here’s why I’m talking to you: there are a bunch of names that are important in my work: Doppler, Euler, Einstein, Fourier. Ignore them; they won’t make a dime off of their work. The other guys: Hollerith and Marconi – follow these guys. Invest in the companies they work for. You won’t be sorry.
Best … Mass Spec … description … Evah!! Can I be your hunchbacked lab assistant?
Oh, my turn. Let’s see, I do management and maintenance on an interactive voice response system for DoD.
Well Mr./Miss/Mrs. 1895, have you heard of the telephone? Imagine you place a telephone call to a special office, and your speak to a person who can help you buy something from a mail-order catalog. Or check on your older orders, or change them, or check stock before placing an order. Sure you could write a letter in the morning and get a reply that afternoon, but what if you needed a reply that very minute? Or if you needed to know after normal business hours? Uncivilized, you say? Well suppose the part was needed for our brave soldiers and sailors and airmen? No, not men made of air - oh never mind.
Anyway, instead of a person, who can only work the usual 16 hours a day six days a week, suppose you needed you answer around the clock seven days a week. Yes, even Sundays. Blasphemous, you say? Well, umm, er, but my damn contract says 24/7 - OKAY!!!
Um, sorry.
Anyway, instead of one person, imagine a team of people - enough to handle DOZENS of calls at a time - working in shifts AROUND THE CLOCK, getting information from other catalogs and form other supply offices all over the country! Except they are not people, they are all Electric Powered Automatons!! Run by the power of the Sun!!
BWAH-hah-HA-hah-hah-HAW!!!
Oh, sorry, got carried away for a moment. It’s not the power of The Sun, it’s five Suns and a couple of Dells.
Beg your pardon? Well, because hiring more people would be more expensive than the automatons. Really.
No, really!
Say, is there a lepidopterist convention around here? Hey put me down! No really, I can explain …
Charles Dickens would understand your job, and approve.
Groo, I’m really interested – what is it that you do? (Radar operator? Radio astronomer? 
)
I work as an intermediary between customers and tradesmen when the former feels that the latter’s work was not properly done and try to resolve their disputes in a civilized manner.
Well, you know how you’ve got taxes, right? Well, There’s a way of adding up all the numbers for each individual person without using your brain (!!!). [del] The people that do the taxes call me up because I help them not use their brain to tell you how much to pay the government.[/del]
No. Wait. That didn’t sound right.
ahem
The people that figure out how much you owe the government then call me to help with how they come up with some of these numbers and how to present them properly to the government.
(I do tech support for a very popular brand of tax software used by professionals.)
Editor, general factotum, and layabout.
I do special effects for video games. I don’t think there’s any way that I could explain that to someone from the 19th century without them tossing me into the nearest insane asylum.
You, uh, you are a Delineator of Optical Amusements.
Well, design real-time embedded software architecture for multi-target tracking modes in airborne radars. I thought that was obvious…
Okay; mostly I argue with people all day long. On the one side there are these fresh-faced Computer Science grads who talk in clicks and pops and whistles, and on the other there are straight-faced analysts who think it’s perfectly fine to ask us to invert a 10000x10000 matrix every 50 milliseconds because it’ll increase our SNR by 0.5 dB. In the middle are people on my team, who rephrase the algorithms into designs that can solved concurrently (dozens or, in one case, hundreds of CPUs running in parallel) with real-time approximations of solutions that don’t offend the analysts too much. And then we have to ensure that the resulting software never halts. Never ever ever. That last is a big deal, because a lot of Computer Science people think that computers are these things that sit on your desk and you can hit CTRL-ALT-DEL if something goes wrong. The pilots, meanwhile, tend to think that if the radar stops functioning, they might not be able to jam the radar of the missile that’s just been launched at them. (Drama queens).
Really strange, specialized job, and I don’t know what I would be doing if it didn’t exist.
Coooool… 
wipes a tear from his eye
My very own hunchbacked lab assistant! Finally, after all these years, I’ve made the big-time at last! Top o’the world, Ma, top o’the world!
Statistical analysis?
Following documented policies and procedures?
Corrective and preventive actions?
Control of non-conforming material?
Management reviews?
Process improvement initiatives?
No way I’m explaining any of that 100+ years ago.
Environmental Engineer dealing mainly in hydrogeology?
I can barely explain the basics of what I do to to my family. I wouldn’t even know where to start 100 years ago.
Mine wouldn’t be hard. Hotel reservations. You call me and if we have a place available when you want to stay with us, I make a reservation for you.
The computer system we use to do this would be the hard part to explain, but not the job itself, as long as we’re talking about late enough in the 19th century that they have phones.
Well given that the civil service was well known and high regarded in 1895 I could say “civil servant” and the person would understand it - I’d then have to spend quite a while explaining the area of work I’m in (children, schools and families) and why we do it given that that social policy didn’t exist in that period, much less anything to do with improving the lot of children so encountering the same problem as Drain Bead.
Telling them that I work in an office where I change desks every day and don’t use paper would see them puzzled. Telling them that my superior is a woman would raise some eyebrows. Telling them that her superior isn’t white would see them completely freaking out.