Yes, and c' is used because the next word starts with a vowel. It is actually ce too, but contrary to English (with it is / it's), you don't have the choice here, and you're obliged to write c'est, NOT "ce est". Ce sont is correct because sont starts with a consonant.
So most of the time you see ', it's an "hidden E". But sometimes it can be an A (l'eau = "la eau"), or an I (s'il te plaît = "si il"). But watch out for si, it becomes s' only in front of an I; si elle CAN'T be "s'elle".