Can someone explain this to me?
Here is what it says in the Bestiary (and the PRD)

Flyby Attack

This creature can make an attack before and after it moves while flying.

Prerequisite: Fly speed.

Benefit: When flying, the creature can take a move action and another standard action at any point during the move. The creature cannot take a second move action during a round when it makes a flyby attack.

Normal: Without this feat, the creature takes a standard action either before or after its move.

The creature can ATTACK before and after a move? Wasn't this always a creature can MOVE before and after an attack? I just keep scratching my head when i read this entry. Please help, my scalp is getting sore.

Without Flyby Attack, a creature's attack and move happen in sequence. One happens first, then the other happens. It can move up to a target and attack, or it can attack a target and then move.

Flyby Attack lets the flying creature make its attack in the MIDDLE of its move. If, say, it has a fly speed of 50 feet, it could move from point A to point B fifty feet away, and make an attack at any target along the way.

Flyby Attack's handy against non-flying foes, really, since you can swoop down using part of your fly speed, attack the grounded foe, then fly back up into the air and out of reach with whatever fly speed for that round you have left.

What James is saying (if I may paraphrase) is that the feat's descriptive text is just that: descriptive text. It's not the rules.

Be that as it may, the phrase before and after it moves should be at any point during its move.

Okay, good. I should just ignore the fluff text and continue to do it like I thought. Good. I assumed this already, but that dang "attack before and after" kept messing with me. I'm better now.

"attack before and after" kept messing with me.

If it says the first, then that needs errata.

the original quote at the top is a direct cut and paste from the PRD. It is the same in the print Bestiary.

This creature can make an attack before and after it moves while flying.

What it's saying is that the attack can be made both before and after it moves while flying. So the creature moves and then attacks after moving (thus the "after" part of the flavor text).

If it continues to move after the attack, then that attack occurred before the rest of the movement. Thus, it's attack was both before movement and after movement.

I agree that there are probably a dozen ways to word it that are much more clear, but I can see the intent.

Greg Kilberger wrote:

This creature can make an attack before and after it moves while flying.

This portion is pretty poorly worded, but if you approach it the right way it can mean what the rest of the rules say.

What it's saying is that the attack can be made both before and after it moves while flying. So the creature moves and then attacks after moving (thus the "after" part of the flavor text).

If it continues to move after the attack, then that attack occurred before the rest of the movement. Thus, it's attack was both before movement and after movement.

I agree that there are probably a dozen ways to word it that are much more clear, but I can see the intent.