Also at 3rd level, you learn to inspire others in battle. A creature that has a Bardic Inspiration die from you can roll that die and add the number rolled to a weapon damage roll it just made. Alternatively, when an attack roll is made against the creature, it can use its reaction to roll the Bardic Inspiration die and add the number rolled to its AC against that attack, after seeing the roll but before knowing whether it hits or misses.

I have a question about the last part. A player always knows his/her character AC. So if the player sees the attack roll, he/she already knows whether it hits or misses. I don't think the last part makes sense and I feel I am missing something here.

they don't know the monster's bonus to hit

As pointed out, you may know the result of a roll (say it's a 12) and your AC (18 perhaps), but you don't know the monsters modifier. If they've got a +5, you're fine. If it's a +6 you're in trouble. It's during that point of uncertainty that you apply the ability. 

and most dms roll behind the screen anyway, so it's all a guess