Answer:
There are three reasons to buy a put option:
to lock in downside profits: if you paid $10 for the stock and it's now $20, you could buy a put at $18. If the stock falls past $18, the put exercises and you keep most of your gain.
in the hedging strategies "straddle" and "strangle." In those you buy both a put and a call.
and to protect yourself against loss: you buy the put at the price you paid for the stock, or at a level you're comfortable with falling to.
You can profit from selling puts in two ways. The simplest is to sell puts that expire worthless, so you keep the premium. The other is in a buy and hold strategy: you buy slightly out-of-the-money puts on stocks that change price in a predictable fashion. You then keep the stock until it goes up in price before selling it. This, however, takes months and if you're into churning stock it will never work for you.