A cytotoxic T cell is a type of white blood cell. It is a T lymphocyte which kills cancer cells, cells infected with viruses, or cells that are damaged in other ways.
Antigen presentation stimulates T cells to become either "cytotoxic" CD8+ cells or "helper" CD4+ cells.
Most cytotoxic T cells have T-cell receptors (TCRs) which recognize a specific antigen from a cancer cell or virus.
Antigens inside a cell are brought to the surface of the cell by major histocompatibility complex molecules, where they can be recognized by the T cell. If the TCR is specific for that antigen, it binds to the complex of MHC molecule and antigen, and the T cell destroys the cell.