"essen" ist the popular description from "to eat". "Das Essen" and "Die Speiße" is similar from sense. "verspeißen" comes from "Speiße". Mostly application of this is on enhanced Situations like Restaurant, Wedding and Meetings. Its more Gentlemanlike ;)

"essen" is less formal whereas "(ver)speisen" (rather "speisen") is quite formal and a bit old-fashioned but still in use, it's often used in written German.

"essen" means "to eat", which is similar to "speisen" (without "ß"), and that is what Эдуард described. "verspeisen" means "to eat sth. up", and that is similar to "aufessen".