The cardinality of a finite set is the number of members that set has. The word 'cardinality' comes originally from the term 'cardinal number', meaning a number like one, two or three, as opposed to an 'ordinal number', meaning a number like first, second or third.
Infinite sets can have cardinalities too.
It is not too difficult to show that the set of integers and the set of rational numbers have the same cardinality. This cardinality is called aleph-null, and it's also not hard to show that it is less than the cardinality of the set of real numbers. There are also infinite ordinals, and depending on how you define them, there are more of them than there are infinite cardinalities, but this is beginning to get beyond the scope of a combinatorics course.