Besides the understandable Wikipedia definition, Video 125. ""Simple Groups - Abstract Algebra" published by Socratica on 2018-01-10." gives an understandable one:
Given a finite group and a simple group , find all groups such that is a normal subgroup of and .
We don't really know how to make up larger groups from smaller simple groups, which would complete the classification of finite groups:
In particular, this is hard because you can't just take the direct product of groups to retrieve the original group: Section 22.214.171.124.6.2.2. "Relationship between the quotient group and direct products".