Lysosomal enzyme: An enzyme in an organelle (a little organ) called the lysosome within the cell. Lysosomal enzymes degrade (break down) macromolecules (large molecules) and other materials (such as bacteria) that have been taken up by the cell during the process of endocytosis.
In endocytosis, macromolecules and particles from outside the cell are taken up by the cell via a progressive invagination (inpouching) and eventual pinching off of a region of the cell membrane, forming a membrane-bound vesicle (bubble) within the cytoplasm of the cell.
The vesicle then fuses with the lysosome and the lysosomal enzymes carry out their appointed task of destruction (by hydrolysis). Quite amazingly, the lysosomal enzymes do not normally damage the cell itself.