how to recognise a broody hen

A broody will sit on the nest all day and all night maybe getting up once a day to defecate and eat/drink, but never lay any eggs. When you get near her or act like you're going to touch any eggs under her she'll screech and maybe try to bite you. It's pretty easy to tell, if you had one you would know it.
 

Before a hen gets serious about being broody, maybe a week before, she begins to pluck the feathers from her breast bone. She also begins to utter the broody "whelp", a low, fussy clucking completely unlike her normal vocalizing. As she gets closer to being truly broody, she becomes very irritable, and often annoys her flock mates with her crankiness. 

Finally, she will lay a final egg and stick to the nest like glue, puffing up and fighting you if you try to remove her, even trying to bite you. 

The reasons people want to break a broody are numerous. They won't lay eggs for the next month. There may also be enough chickens in the flock that more chicks are not needed. A nesting box will be tied up for a month for no good reason. So, we choose to break our broodies for these reasons, not because we don't "like" broodies.

They have pretty much explained it. Although, sometimes, a broody will just go straight to laying on eggs without any signs. For example. I had a broody who layed an egg everyday and I would collect them everyday. She didn't show any signs whatsoever. Although, I had another broody, who started walking around clucking like a broody with her wings spread out and getting mad at anyone who got near her. This happened about 5 days before she actually went broody. Although, like azygous said, it is not always a bad thing. I was really happy when my hens went broody, I've now got 3 day old chicks and nine more coming :D