I just learned about this from NPR today. It started in the late 19th century, when the lakefront mansions were only accessible by boat. Mail is delivered by a a “mail jumper” who jumps from a moving boat onto the dock, delivers the mail and collects outgoing mail, and jumps back on the boat, all while the boat continues moving. Although the houses are all accessible by road now, they’ve maintained the tradition.
And a video if you want to see them in action
Some years ago there were some mail routes that still delivered by boat, and mule - at Grand Canyon national park.
Ok, apparently editing my post to say I fixed the embedded video broke the embedded video. Let’s see if this works.
No… Ok, fine, here’s a link again.
ETA: And now the embedded video in the OP magically fixed itself.
I heard that report on NPR and thought that it sounded like fun. Though I don’t have the agility to actually do that job.
If you search YouTube for fail videos, examples of amateurs trying this trick seem to feature prominently.
I don’t any more but as a teen, I would have done a great job.
This got me thinking about how they deliver the mail to the Northwest Angle of Minnesota. Turns out, it is done by car, through Canada, from Warroad. The NW Angle does have its own tiny post office.
Gotta be tough jumping in and out of moving cars. You don’t just get wet if you miss.
Tom Scott did a video and tried it himself last year:
This was one of my mom’s favorite outings.
Her international and even cross-country trips are behind her now (she’s in her 90s), but she loves to get driven around to interesting places. So we did a trip to Lake Geneva*, and she LOVED the Mailboat Ride. You get to watch those high schoolers up close, and hope they make it (they’ll jump off the bow, fill a dozen mailboxes on a long pier, then race as fast as they can to do a long jump onto the stern of the boat.
*Read up on the history before you go. A train line was constructed from Chicago to the lake, and when the Chicago fire razed many homes, like those of the Macy and Wrigley families, they took refuge on the shores of Lake Geneva. It’s so cool to see those ancient mansions from the lake.
That’s where I recently learned of this “job”. Looks like it would be fun…for a bit at least.
What’s a little road rash? 
Still do, as far as I know. I hiked across the Canyon some years ago. There’s a small lodge at the bottom, and you can buy and send a postcard, but I didn’t. I think there might be a special postmark.
Is there any particular reason the boat has to be moving?
It would take a lot more time for them to have to stop and start at each place.
Granted, the actual service isn’t really needed anymore. It’s more a fun tradition. But that was the original reason.
It’s also pretty dangerous. A fine example of a tradition that shouldn’t be around anymore.
What’s the danger? If you land in the lake, you swim. I would hope that only strong swimmers would be doing this.
The Teen Mail Jumpers from Lake Geneva, Wisconsin
You can tell I live in Chicagoland because I immediately thought the thread title referred to juvenile criminals jumping and mugging mail carriers. LOL
Yes, we actually have that, too. 
Well, let’s see… you’re bringing a decently sized boat (for lake purposes) along side a dock, so off the top of my head, having spent many years working around boats and docks… Someone could fall between the boat and the dock and be crushed. There are, presumably, propellers driving the boat, so that’s a danger to anyone who ends up in the water. Boats may have underwater intakes, generating suction, which—depending on the strength—could be enough to trap someone to the hull underwater. And… the boat itself. You could be struck in the head by the very heavy boat moving through the water right next to you.
And that’s ignoring the danger of running on a wet/slick dock. Like, I’m just focusing on the boat right now.
Nothing about this is safe. It’s a great example of how flipping dangerous life was a hundred years ago, and why safety regulations are a good thing.
And of course, that is exactly why the teens like the challenge. They get to show off athleticism, daring, and practice skills that will serve them in future jobs too. They aren’t worried about slivers, sprains, bruises, or dangerous lake water. If this wasn’t a paying job, they’d be doing it without the job because teens. I grew up lakeside. We did insane things if we knew we wouldn’t get caught. This one is relatively mild.
Yet many of us ride motorcycles and bicycles. I wonder what the death toll is for the mail jumpers vs those far more common activities (even averaged out to number of deaths per thousand participants)? Heck, I live near Spokane, WA and it seems at least one pedestrian is sadly killed each week in that town. I would speculate that walking in Spokane is more dangerous than mail jumping.