Besides the understandable Wikipedia definition, Video 160. ""Simple Groups - Abstract Algebra" by Socratica (2018)" gives an understandable one:

Given a finite group $F$ and a simple group $S$, find all groups $G$ such that $N$ is a normal subgroup of $G$ and $G/N=S$.

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 "Relationship between the quotient group and direct products".

- Classification of finite groups | 77, 357, 6
- Normal subgroup | 149, 554, 8
- Quotient group | 51, 977, 11
- Subgroup | 0, 977, 13
- Group | 0, 1k, 28
- Algebra | 0, 2k, 56
- Mathematics | 17, 13k, 329
- Ciro Santilli's Homepage | 262, 181k, 3k