The Nine Realms, or Nine Worlds, or Nine Planes are:
Alfheim, Asgard, Hel, Jotunheim, Midgard (Earth), Muspelheim, Nidavellir, Svartalfheim, and Vanaheim(*).
The Big Tree is called Yggdrasil.
As for explaining what they are, and their inter-relation – especially in the context of the Marvel version of Thor – I could grab my crayons and do my best, or simply link to the excellent Wikipedia entry on the subject here:
(* Am I really the only one who had to memorize this in the third grade?!? )