The End Phase is the final phase of the turn. It is conducted after Main Phase 2 or Main Phase 1 if you did not conduct your Battle Phase, or after your Battle Phase if you did not conduct your Main Phase 2.
Effects apply during the End Phase
Many Card Effects apply during the End Phase, such as "Brain Control". The turn player gets to decide the order to apply their maintenance costs and/or Effects that apply or activate at this time.
Hand Size Limit
At the end of the End Phase, if the turn player has more Cards in their hand than the hand size limit (normally 6), they must discard Cards until their hand satisfies the hand size limit.
At the End of the Turn
Any action that states "at the end of the turn", such as the expiration of the Effect of "Effect Veiler", is done at the very end of this phase after discarding Cards to adjust for the hand size limit if the number of Cards exceed this.