What function does lysosomes perform in a cell?

Lysosomes degrade proteins. The kind of proteins they degrade are brought into the cell by endocytosis - they do not degrade proteins that are resident in the cell, proteasomes do that . Lysosomes fuse with the protein to be degraded and release the special class of enzymes they carry, hydrolases, that do the actual break down process. Lysosomes are also the key factor in ridding a cell of H2O2 in a cell, hence the hydrolases.