제대로 means properly, in the right way, the way it should be, etc. It is 제 + 대로, where 대로 is a suffix meaning "the way it is (not trying to change it)". So 이대로 means "the way this is now", and 그대로 "the way that/it is now". 제 is a short form of 자기 (self) among others, so 제대로 is like "the way its proper self should be", which means "in the proper way". You can think of phrases like: 제대로 해! (Do it the proper way!), 제대로 된 연애(a relationship that is right), etc.

properly