"ese" is a demontrative adjective, so in cases where this word is followed by a noun, no accent is required: ese edicio, ese banco etc. "ése" is demonstrative pronoun, so in cases where the noun is missing right after the word, an accent is present: ése es un banco; qué es ése? However, it seems that according to the new spelling rules, no accent is needed anymore.

Dan gave an excellent answer, I'll try to complement him: Ese edificio = That building. "Ese edificio es el banco" =That building is the bank Ése es el banco= That one (that building) is the bank.