Definition:System of Sets

Definition
A system of sets is a set whose elements are themselves sets.

Those elements are usually assumed to be subsets of some particular fixed set which is frequently referred to as the universe.

Note
Some authors are more explicit with their use of a universe and may say "Let $\mathbf X $ be a system over $X$".

This just means that $\mathbf X$ is a set whose elements are subsets of $X$.