This phrase is typically used in response to someone exclaiming, "It was close!" The idea being that while close may be of value in other fields (e.g. the game of horseshoes), it is worthless when you get a question incorrect on Jeopardy! or miss landing on a skateboard ramp when flying through the air.

More modern (and more cynical) variations include "close only counts in dancing" or "close only counts in horseshoes, hand grenades and atom bombs."¹

Typical dialog:

Regis Philbin: So you're going to make that...
Contestant: Yes, D is my final answer.
Regis Philbin: Oh, no! The answer was C. The audience was right, after all! You walk away with only $64,000.
Contestant: Well, I was close.
Regis Philbin: Unfortunately, close only counts in horseshoes.

¹ Thanks, Coach Gann.