You usually say this when you are doing laundry or when something happens that causes a stain on an article of clothing. For example:

"Look at all those kids playing soccer! That one just slid into the net, giving his shorts a grass stain. I am sure one of his parents will be able to wash it out"

"Tomato stains are the most difficult stains to wash out."

You have two options (that I can think of):

1. to wash something out of something (esp. hair, clothes)

eg. I've been painting and some got in my hair, so I'm going to try to wash the paint out of my hair.

2. to wash out a container (to clean the inside of it)

eg. After you've used the bucket, you should wash it out.

Bonus: when a child is swearing, old fashioned parents might threaten:

"If you say that again I'm going to wash your mouth out with soap!"

My grandmother actually used soap to clean inside of my mother's mouth!