At the end of the day is an idiomatic expression meaning “ultimately”, “in the end”, and it also often has a flavour of “after all”. For example:
You don’t have to clean your room, but at the end of the day it will be you who will have to live in a mess.
Workers staggered around, half-drunk, taking with them at the end of the day everything they could carry—doorknobs, faucets, nails. [From A Mountain of Crumbs by E. Gorokhova]
By the way, if you haven’t read my guide on how to avoid the most common mistakes in English, make sure to check it out; it deals with similar topics.