Besides the understandable Wikipedia definition, Video 135. ""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 | 71, 312, 5
- Normal subgroup | 143, 503, 7
- Quotient group | 45, 916, 10
- Subgroup | 0, 916, 12
- Group | 0, 2k, 47
- Algebra | 0, 2k, 65
- Mathematics | 17, 10k, 239
- Ciro Santilli's Homepage | 238, 147k, 2k