The most notable attribute of 1.e4 is that it commences an immediate fight for the center. If allowed to do so, White will play 2.d4, occupying the central squares d4 & e4 and controlling four squares on Black's side of the board : c5, d5, e5, & f5.
Black must react to the threat of 2.d4, or risk getting an inferior position after the first few moves. The adequate responses to 1.e4 can be divided into two types -- moves which delay an immediate 2.d4 (1..e5 and 1...c5) and moves which allow it (all other moves). We'll look at each type of move separately.
Responses to 1.e4 which delay 2.d4
In fact, none of Black's responses to 1.e4 prevent White from playing 2.d4. The d-Pawn, protected from behind by the White Queen, can safely advance to d4 after any first moves by White and Black. The moves which delay 2.d4 are played to take the sting out of it. If White insists on responding with 2.d4, Black gets good compensation.
