Autolysis is the breakdown of a cell's components by its own enzymes. In winemaking and brewing, yeast-cell breakdown releases compounds that affect flavor and body. It can be desirable during some lees-aging processes and undesirable in other circumstances.
Do not confuse it with bread autolyse, a rest of flour and water before the remaining dough ingredients are added. The similar name does not mean that yeast-cell breakdown is the purpose of the bread rest.
Reference: Further reading.