Extinguish, as in We put out the fire before we turned in. [Early 1500s]
Also, put to sea. Leave a port or harbor, as in They put out yesterday morning. [Late 1500s]
Publish, as in They put out a weekly newsletter. [Early 1500s]
Engage in sex. This usage is applied solely to women, as in She had a reputation for putting out. [Vulgar slang; mid-1900s] Also see put one out.