Set a is a subset of set b, expressed as means that

You express that A is a subset of B with the following expression:

The meaning is that A is fully included inside B, which in turn means that every element of A is also an element of B, while the vice versa is not necessarily true.

For example, consider the sets

So, B is the set of numbers from 0 to 10, and A is the (sub)set of all even numbers between 0 and 10.

So, A is a subset of B, because every element in A is also an element in B, but there are elements in B (all the odd numbers) that are not in A.