From the Oxford English Dictionary: homophone: noun each of two or more words having the same pronunciation but different meanings, origins, or spelling (e.g. new and knew). ORIGIN from Greek phone ‘sound, voice’.
There are many, many of these in the English language, and they're really easy to abuse.
its: belonging to it, whatever "it" may be.
Daniel had never seen an alien with its face in such an...interesting place.it's: a conjunction form of "it is," "it was," or "it has"
"Oi, Moony, come outside," Sirius said, stumbling into the common room. "It's snowing!"
It's not the first time Daniel's given him the silent treatment, and Jack was sure it wouldn't be the last.
"It's been two hours," John said, spinning his chair to face Rodney. "You sure you're not done yet?"[A hint: to make sure you're using the right one, try breaking "it's" into "it is," "it was," or "it has" and see if the sentence still makes sense.]
your: belonging to you
"Ah, Jack? Your fly's open."you're: a conjunction form of "you are"
"You're standing on my robes," Lily said, and James blushed and jumped back.[A hint: like "it's," "you're" can be broken down into "you are" to make sure you're using the right homophone.]
Mistakes happen; the best way to check for homophone abuse is very careful reading and one or two nitpicky betas. And there's always one that sneaks past, but such is life.
(For other homophone help, see green_grrl's post on two/too/to and there/their/they're.)