Catnip is a recreational herb for cats.  It is the scent and not the consumption of it that has a dramatic effect on cats, but cats are known to eat it while enjoying it.  It is not known for sure what happens in a cat's brain, but we do know that the chemical nepetalactone in catnip is the thing that triggers the response.  Most cats begin to react to catnip at six to eight weeks, but some cats do not react all (very young kittens and older cats seem to have less of a reaction).  Large cats, such as tigers, can also be affected by it.  The reaction only lasts for a few minutes, and then the cat may lose interest in it.  It then takes about one to two hours for the cat to "reset" and be affected by it again. 

When affected by catnip, your cat may exhibit some of the following signs:  purring, cheek rubbing, licking/eating the actual cat nip, body rubbing, grasping at object that smells like catnip, kicking.  They'll get very friendly and rub against you, and may give you "love nips" if you are interacting with them while catnip is present.

Because catnip is part of the mint family, you may notice that your cat also really enjoys the smell of peppermint.  I have peppermint foot lotion from The Body Shop, and when I put it on my cats try to burrow into my socks.