The concept of infinity has fascinated humans since ancient times.The first known reference comes from the 5^th century B.C.E. Wikipedia presents many interesting facts and applications of the concepts of both potential infinity (as used in Calculus for example) and actual infinity (as used in Set Theory).
Dennis Wildfogel also created an original TED-Ed lesson on the concept of actual infinity. You can watch it here.
Another great place to watch videos on infinity and other number related concepts is Numberphile.
Here are a few of their specific videos dealing with infinity, prime numbers, etc.:
http://numberphile.com/videos/countable_infinity.html
http://numberphile.com/videos/infinity_paradoxes.html
http://numberphile.com/videos/infinite_primes.html
http://numberphile.com/videos/zeno_paradox.html
In addition to online resources, there are also some outstanding books dealing with the concept of infinity. Here is a very short list that I would highly recommend:
The Infinite Book: A Short Guide to the Boundless, Timeless and Endless by John Barrow
The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity by Amir D. Aczel
To Infinity and Beyond: A Cultural History of the Infinite by Eli Maor

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