Surah Al-Kahf 18:9-22: What is this story about youths in a cave?

I have been reading Surah al-Kahf and I find myself quite confused about ayat 9-22. What is this story about youths in a cave? It is presented like it should be a story that I am already familiar with, but I am not. Especially in ayah 22 where it gets into a discussion about how many youths there were and whether or not the dog counted among their number. Could someone help lend some background and context to this?