"Taildragger" is the pilot's way of referring to an airplane with the third wheel at the tail, instead of the front. That's how all airplanes were built until WWII, when some bright spark had the idea of putting the third wheel up front. That arrangement, called "tricycle" gear, is a lot more controllable and easier to handle on the ground - including when the airplane first touches down after landing. The difference is that the airplane's center of gravity is forward of the main gear in a tricycle airplane, and behind it in a taildragger, which makes the taildragger want to swap ends if you aren't paying attention.
Lots of pilots learned to fly in taildraggers. They haven't been in common production for many years, though, except for kit planes and modern reproductions of classic aircraft. I'd never flown one until yesterday. I'm used to airplanes that go right where you point them, on the ground or in the sky. That's not how you'd describe a taildragger on the ground...and how you point it in the sky is a lot different.
On the ground, a tricycle gear aircraft is usually steered by turning the nosewheel. It's connected to the rudder pedals, so you press on the right pedal to turn to the right. The result is usually quick and predictable, and easily mastered. A taildragger is steered on the ground by either turning the tailwheel or using aerodynamic forces on the rudder itself. Neither is very responsive, and you have to stay two steps ahead of the aircraft. To make matters worse, a taildragger is much more ready to fly on the ground than a tricycle gear airplane, because the wings are tilted upward, so you have to pay close attention to the wind direction and apply control inputs to keep the airplane firmly planted; it's a good idea in a tricycle gear airplane, too, but nowhere near as critical.
In the air, the gear itself doesn't make much difference, but the rest of the characteristics of a classic taildragger like the Taylorcraft BC12-D I was flying come to the fore. They're bigger than more modern airplanes, and the controls aren't nearly as well harmonized; the ailerons are also bigger and much farther away from the aircraft's centerline. That means that you have to pay much more attention to using the rudder to keep the nose pointed in the direction you're going. My turns were sloppy, and an attempt at a ground reference maneuver (where you fly a prescribed path along the ground) didn't turn out as well as I'm used to doing in my airplane.
Landings are where most new taildragger pilots come to grief, and I was no different. I got around the pattern in decent shape, but once I rolled out on final, I couldn't keep it pointed down the runway or over the centerline to save my neck. I finally gave up and let the owner show me how it was done.
The rules were changed in the early 1990s to require that a pilot who hadn't logged any taildragger time before then to get a signoff from an instructor before flying one. That signoff reportedly takes most pilots from 6 to 10 hours. I can see why, now. I want to get one, because I think it'll improve my flying all the way around, but it's not going to be trivial.