In mathematics there are esentially two types of sets - those that are countable and those that are uncountable. A set is said to be countable if and only if its members can be put into one and one correspondance with a subset of the natural numbers. Note that many sets that are infinite are still countable - for example the set of even numbers. An example of an uncountable set would be the powerset of natural numbers - this can be proven using Cantor's diagonal argument.
