Golf holes are designated a par 3, par 4 or par 5 (and rarely par 6), meaning that three strokes, four strokes or five strokes, respectively, is what an expert golfer is expected to need to complete play of that hole.
So an eagle is:
- Scoring a 1 on a par-3 hole (a k a, a hole in one)
- Scoring a 2 on a par-4 hole
- Scoring a 3 on a par-5 hole
Eagles are most commonly made on par-5s, holes on which some golfers who hit the ball far can reach the green in two strokes, then make the putt.
Eagles on par-4 holes are much rarer because they require either driving the green and 1-putting, or holing out an approach shot from the fairway. And, as noted, an eagle on a par-3 is a hole-in-one (nobody ever calls those eagles, however - why would you call it an eagle when you can call it a hole-in-one instead?).