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This documentary is more about the consequences of the idea that the universe is infinite and theory of cosmological inflation of the universe, than "what is an infinite number or infinity?" However you have to wade through some of the more juvenile content to get to the good stuff.
Be patient.

By our third year, most of us will have learned to count. Once we know how, it seems as if there would be nothing to stop us counting forever. But, while infinity might seem like an perfectly innocent idea, keep counting and you enter a paradoxical world where nothing is as it seems.

Mathematicians have discovered there are infinitely many infinities, each one infinitely bigger than the last. And if the universe goes on forever, the consequences are even more bizarre. In an infinite universe, there are infinitely many copies of the Earth and infinitely many copies of you. Older than time, bigger than the universe and stranger than fiction. This is the story of infinity.

Learn more about physics, cosmology, the physics of the very large, and quantum mechanics, the physics of the very small, and the physics of everything in between at PhysicsWizard.com.