Breeches is a somewhat old-fashioned word for trousers, and one you probably don't need to deploy often unless you're heavily into riding gear or have scored a job writing Asterix comics. One context where you definitely shouldn't use it? When you actually mean breach.
Tear picture from Shutterstock
Sadly, you don't have to look too far to find sites discussing "data breeches", such as this post from Xconomy.
Breeches is one of just a handful of words in English with -eech endings (others include leech and beseech), while -each is far more common. So choosing breech when you mean breach is an error that can't be readily excused. Accuracy matters.
Lifehacker's Mind Your Language column offers bossy advice on improving your writing.