This is dumbed down a bit, mainly cause I am too dumb to explain it in more detail. The technique is more accurate than my description below.
All carbon atoms have six protons (and chemically, this is what makes it carbon). Most carbon atoms also have six neutrons and thus have a mass number (protons plus neutrons) of twelve. But some carbon atoms have seven neutrons, and a few have eight neutrons. Thus, some carbon atoms have mass numbers of 13 and 14. When you see a mass number on a periodic table, it shows the “average” mass number of carbon is 12 plus small change, as there are not that many carbon-13s and carbon-14s.
Radiocarbon dating relies on the fact that carbon-14s tend to break down slowly over time, that is, they have a long half life of some 5730 years or so IIRC. When a plant or animal dies, it stops replacing its carbon. The number of carbon 14s from a sample can be measured and compared to the number found in living material. These values are points on a decay curve which can be easily manipulated to find the difference in time between now and the date the plant or animal died.
Of course, this is based on accurate measurements of the carbon 14, and the validity of the assumption that no new carbon 14 is in the material. It also assumes that an average measurement of carbon 14 in currently living material is indictive of most items. These assumptions may be broad enough to make some question the accuracy of the technique. Newer techniques do not make as many assumptions as when radiocarbon dating was first discovered.
The reason it is accurate is that we know the exact half life (rate of decay) of carbon 14, 5,568 years (trust me on this)
The moment a living thing expires, it begins to lose C14 at a constant and measurable rate. Thus by calculating the differential between C14 in the environment and that left in the dead thing, we can make the calculation of how long it has been dead.
It is very accurate but given the magnitude of the time you are measuring, either very long (eons) or short (seconds), rounding can have a very large effect.
Why do some people say it’s not accurate? Maybe they think that the margin of error is too great. But I suspect that the dates derived from carbon-14 may clash with their beliefs. For example, some people may believe that the Earth is only 6,000 years old. How, then, can anything possibly be carbon-dated at 100,000 years old unless carbon dating is inaccurate? Or someone may find a fossil that he believes is 500,000 years old, but carbon dating puts it at an earlier date and destroys his theory. Not being an archaeologist or physiscist, I’m just guessing though.
I don’t believe we don’t know the exact half life of carbon14, but that is a very good figure. Some put Carbon14’s half-life at 5,730 years. It could be I haven’t kept up with the latest. Anyway, Carbon14 is accurate to within 1-2%. This margin of error being given to it due to half-lives and the knowledge of decay constants having some uncertainty in it. It was certainly good enough for 3 independent labs to date the Shroud of Turin.
No credible scientists AFAIK, doubts it accuracy. Some with religious agendas such as ultra-conservative Christians have a beef with it because it goes against their young earth of about 6,000 years.
Johnny L.A. 's link above is a pretty good intro, but misses one difficulty.
C14 is formed by cosmic rays hitting the atmosphere, and the intensity of cosmic rays varies quite a bit, so a sample’s initial concentration of C14 also varies. This of course throws off the value we measure.
To get an accurate calendar age, we have to apply a calibration curve to adjust our measurements. The curve is made by measuring samples of a known age, often from tree rings (which can be pieced together to get dates going back several thousand years) or from marine sediments that show seasonal layers.
See http://www.c14dating.com/ for more detail than you want. There’s a Calibration link on the front page.
As I understand it pretty much yes. C14 is created in the atmosphere by cosmic rays. Plants take this in as C02 when they make sugar through photosyntesis. Animals get their carbon from plants. If an organism uses non-atmospheric carbon(Like calcium carbonate for shells of some sea animals.) then you can’t use C14 to date it.