So basically if you are a Market Maker and you sell an ATM option, you don't really want to take a directional view on the stock. You just want to make money on the bid/offer spread. Actually, you hope that the guy who bought the option makes money so that he can come back to you and unwind the trade for more profit.

Problem is, you are now short an option that makes money if the stock goes one way, and loses money if the stock goes the other. So what do you do? You even out that profit distribution a little bit by trading some stock against the option. This way, if it goes ITM you have some protection, and if it goes OTM you lost some potential upside but you might still make money if the option doesn't move very far.

Hedge funds don't usually do this (although they might use it to lock in profits before a reversion), because they use options to take directional bets. Some of them do take bets on volatility, but not usually the big famous ones.

Delta hedging is really easy to do. If you think a put is cheap and you think the stock is going to move -- but you're not sure about the direction -- you can buy the put and buy the same number of shares as the delta. 30d put? 30 shares. You always hedge the same direction for a put, and the opposite direction for a call. Long put long stock. Short call long stock.