T cells are a class of leukocytes that play a large role in the secondary immune response. "T" is the abbreviation of the thymus, the organ in which their development ends.
They are responsible for cellular immunity: cells infected with a virus, for example, or cancer cells are known to be foreign to the body (that is, distinct from the cells that T cells have learned to tolerate when maturation) is destroyed by a complex mechanism.
T-cell needs the antigen MHC I molecule (present in all the nucleated cells), to be activated.
While The B cell needs the antigen presented by MHC II molecule present in antigen presenting cells.
T-cells bind 1 type of antigen (which is an endogenous antigen, as opposed to B cell which bind exogenous antigen) which must be presented by another cell.