A hole's par count is determined by what is deemed the most appropriate number of shots taken to complete the hole.
Par 3 signifies that the hole should take 3 shots, par 4 in 4 shots, and par 5 in 5 shots.
In other words, the par count indicates the length and difficulty of the hole in play.

Additionally, the par count in relation to the number of shots taken determines the player's score.
For example, if the player holes out in 3 strokes on a par 4 hole, this results in a birdie (or 1 under par).
If another golfer holes out in 5 strokes on the same hole, this results in a bogey (or 1 over par).

Like the example above, each score has a different name in golf.
The ones in use for the game are as follows:

Birdie : 1 under par
Eagle : 2 under par
Albatross : 3 under par

Par : Stroke count equals the hole's par count
Bogey : 1 over par
Double-bogey : 2 over par
Triple-bogey : 3 over par