T-Tops are a kind of removable panel that some cars have on the roof, like a sunroof that goes all the way across. This is a low cost alternative to the more expensive convertible top. Some vehicles were available in both configurations. This has most of the same fun-factor of having a convertible roof, at least from the driver's point of view. But the back seat passengers don't get that complete open air experience that only a real convertible can offer. One advantage to T-Tops is that they are much safer in the event of a rollover, as you still have a rigid roof over your head.
When you take your T-Tops out the area directly above your head is open to the air, except for a small bar in the middle going from the windshield to the back part of the roof. Targa tops are the same thing but without the bar.
T-Tops were most common on the Camaro, (and all its variants), but were also available on Mustangs, RX7s, Dodge Chargers, Subaru Brats, Buick Regals and a many others.
T-Tops are notorious for being lost, broken, or stolen. This keeps replacement units for all vehicles in constant production. They are also easy to find in the classified ads. But the ones you see in the classifieds are often advertised by the same people who stole them in the first place. Over time, they tend to develop leaks around the seals, which are very difficult to properly repair (even more so than fixing a convertible top leak).
When buying a car with t-tops you should always assume that they leak. No matter what the previous owner tells you. If it is an older car, then they probably already leak. If it is a newer car, then they will leak eventually, just give them a few years. Simply select a different vehicle if you can't handle a bit of water on you from time to time. Because a car with t-tops that don't leak is a very rare thing indeed. Those few that don't leak are often cases where the t-tops were rarely (if ever) removed, and if you start using them, then they will quickly develop leaks. A new set of seals will sometimes fix the problem for a few years, but never eternally.