Par 3's are the shortest holes on a regular 18-hole golf course. The idea of a par 3 hole is that you should be able to get your ball safely on the green from the teeing ground. You should then be reasonably expected to take no more than 2 putts to get the ball in the hole. Thus, a normal score on the hole for a decent golfer would be a 3.
Obviously, these are the holes which will occasionally bend to the will of the golfing gods and give up a hole in one. A hole in one is just an eagle (two strokes under par) on any other hole, and there really is no more majesty in a hole in one than there is in an eagle on a par 4 hole. In fact, one could make the case that an eagle on a par 4 is harder because you would be hitting your second shot from a lie you cannot control. On a par 3, you can tee the ball up or place it wherever it suits you. An eagle on a par 5 is not all that uncommon, especially these days with the modern golf equipment and the souped up golf balls. (One can only wonder at how the real legends of golf, like Bobby Jones, would have played with all the high tech stuff on the market nowadays.) The real feat in golf is the double eagle; three stokes under par on one hole. This could be a hole in one on a par 4 but is more likely holing out in two on a par 5.
A golf course which is a normal championship course will normally have a par of 72. This course would normally include four par 3s, four par 5s, and ten par 4s. The length of the par 3s from the men's tees would normally be somewhere between 100 yards to 200 yards. Par 3 holes often have water or other hazards somewhere between the tee and the green in order to penalize those players who have a hard time getting the ball airborne.
Some of the more famous par 3s are Number 17 at Augusta National where the Masters is played and the island 17th green at TPC at Sawgrass where the Players Championship is played. Hitting a golf shot into an island green is one of the scariest shots in all of golf because there is nowhere to bail out. You either hit a good shot or you are faced with the same shot again. This is when it's time to put up or shut up when you're playing golf for a little money with your friends, and even more so when you're doing it to try to make a living.
Sometimes you will find a golf course made up entirely or primarily of par 3 holes. These are often referred to as Executive Courses and are usually tied in with other regular courses as a place for either the novice golfers (hackers) or the busy executive to get in a quick round. They are also a great place to go play a few rounds in order to work solely on your short game.
There is an old story about a golfer who was so used to cheating that one day, when he finally made his first hole in one on a par 3 hole, he wrote down -0- on the score card.