A kind of immune cell. Named after the fact that they develop in the thymus.
T-cells and B-cells make up the acquired immune system.
T-cells have T-cell Receptors, which are called TcR. Unlike antibodies that can directly bind to their antigen, T-cell Receptors bind their antigen when it is bound to another receptor, called the MHC (for Major Histocompatibility Complex, for historical reasons). T-cell antigens are usually short peptides (which are short proteins).
They are divided into two main groups. CD4 T-cells have the protein CD4 on their cell surface. CD4 T-cells participate in immune responses by secreting various cytokines and helping in the maturation of B-cells. For example, an immature B-cell binds to a piece of bacteria, internalizes this piece, and presents a part of this piece on it's surface. A CD4 T-cell comes around, and if it recognizes this piece, it means that there's an infection. Chemicals that help deal with infections are released, and this CD4 T-cell will help in the maturation of this particular B-cell that has the correct antibody to produce more antibodies.
CD8 T-cells have (you guessed it) the protein CD8 on their surface. CD8 T-cells participate in immune responses by killing cells that have their antigens on them. An example of how this would work is that a cell in your body would get infected by a virus. The virus starts making it's own proteins in one of your cells. Eventually, these proteins make new virii, and kills that cell, and the new virii spread. While the virus is making viral proteins, some of the pieces get presented on the surface of the infected cell. If the correct CD8 T-cell comes by and recognizes this piece, it'll kill the infected cell before new virii are made, and simultaneously kill the virus infecting that cell.
All this is vastly oversimplified.