Besides the understandable Wikipedia definition, Video 171. ""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 | 69, 1k, 27
- Normal subgroup | 149, 1k, 30
- Quotient group | 51, 2k, 33
- Subgroup | 0, 2k, 35
- Group | 0, 5k, 89
- Algebra | 0, 8k, 171
- Mathematics | 17, 28k, 633
- Ciro Santilli's Homepage | 262, 218k, 4k

- Classification of finite groups | 69, 1k, 27
- Relationship between the quotient group and direct products | 308
- Semidirect product | 441