Logically, if 75 moves have been played, 50 moves would've also been played. This sounds ridiculous. It is like saying "I would buy this book if it cost under $60 and it costs under $40". So, what is the logic behind that?
From the FIDE Laws of Chess:
9.3 The game is drawn, upon a correct claim by a player having the move, if: (...) the last 50 moves by each player have been completed without the movement of any pawn and without any capture.
9.6 If one or both of the following occur(s) then the game is drawn: (...) any series of at least 75 moves have been made by each player without the movement of any pawn and without any capture.
As you can see, the decisive difference is that the 50-move rule only applies if a player correctly claims it, while the 75-move rule applies independently of any claims. So, in the 50 to 75 move window, the players can claim for a draw, but don't have to (and play on). Only when the 75th move without pawn moves or captures has been reached, the arbiter may interfere and declare the game drawn.
Although the responses all were intended to answer the question, they all fell slightly short. The 75-move rule was implemented so that an arbiter could adjudicate a game as drawn in a clearly drawn position when both players were electing to play on, hoping that their opponent would falter. Usually in cases where a draw was as good as a lost for both players, i.e. a win would secure prize money, a draw would win no prize money. Arbiters have a life too. ;>)