Start with par, because all golf scoring terms are defined in relation to par. "Par" refers to the number of strokes an expert golfer is expected to need to complete the play of one hole on a golf course (or of the full golf course, but the one-hole definition is the one that is relevant here).
Golf holes of different lengths will require more or fewer strokes by a golfer. And regardless of length, the par number of a hole always allows for two putts. So a 150-yard hole is one on which the expert is expected to hit the green with his tee shot, take two putts, and, therefore, require three strokes to finish that hole. So that hole is designated a par-3.
A very good golfer - or a very lucky golfer - might complete a hole in fewer strokes than the par. And of course, most of us aren't "experts" at golf, and so on most holes we'll need more strokes than the par.
That's where those other terms - birdies, eagles, bogeys, et.al. - come into play. They describe a golfer's performance on a hole in relation to the hole's par. If you make a birdie, you've finished the hole in one stroke fewer than par (a k a, 1-under par). Make a bogey and you needed one more stroke than par (a k a, 1-over par).
Let's say you are playing a hole that is a par 5. Here is what those scoring terms mean on a par-5 hole:
- Eagle: On a par-5, means you finished the hole in 3 strokes
- Birdie: You finished the hole in 4 strokes
- Par: You finished the hole in 5 strokes
- Bogey: You finished the hole in 6 strokes
- Double bogey: You finished the hole in 7 strokes
- Triple bogey: You finished the hole in 8 strokes