A T-tail is a type of empennage where the tailplane (horizontal stabilizer) is mounted to the top of the fin. Observed form behind, this looks like the capital letter T. Sometimes the term is used to refer to an aircraft with such empennage.
An example of a T-tail aircraft
The main advantage of a T-tail is that during normal flight conditions the elevator is above most of the effects of downwash from the propeller (in case of a propeller-driven aircraft) and the airflow around the fuselage and wings. Elevator operation in undisturbed air allows control movements that are consistent throughout most flight regimes.
The t-tail is a popular design in aircraft with aft fuselage mounted engines (e.g. MCDONNELL DOUGLAS MD-82) because it removes the tail from the exhaust blast. Seaplanes and amphibian aircraft (e.g. BERIEV A-40 Albatross) often have T-tails in order to keep the horizontal surfaces as far from the water as possible.
The main hazard with this design is the possibility of entering a Deep Stall. While this can occur on other aircraft as well, the risk is greater with T-tails as a high AOA would likely place the wing separated airflow into the path of the horizontal surface of the tail. This may result in loss of elevator authority and consequently, inability to recover from the stall (i.e. Loss of Control).