The subset relation defines a partial order on sets. In fact, the subsets of a given set form a Boolean algebra under the subset relation, in which the join and meet are given by intersection and union, and the subset relation itself is the Boolean inclusion relation.
A subset, as the name suggests, is a subcollection of any set. Let us assume we have two sets, X and Y. Mathematically speaking, X will be a subset of Y if and only if all the elements of X are present in Y.