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To elaborate:
The set of integers is infinitely large. Subsets of this set, e.g. all the odd integers, are also infinitely large, they are the same size as the original set. This kind of infinity was called aleph-null by Cantor.
As ADT pointed out, there are an infinite number of real numbers between every integer, so the set of real numbers is infinitely bigger than the set of integers. Cantor called this aleph-one.
This process can continue as well. By taking the power set (the set that includes all the subsets) of any infinite set, you get an infinite set that is infinetly bigger! For example, the power set of the set of all real numbers would be aleph-two, its power set would be aleph-three, and so on.
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