I do this often with shares that I own - mostly as a learning/experience-building exercise, since I don't own enough individual stocks to make me rich (and don't risk enough to make me broke).

Suppose I own 1,000 shares of X.  I don't _expect_ my shares to go down, but I want to be compensated in case they do go down.  Sure, I could put in a stop-loss order, but another option is to sell a call above where the stock is now (out-of-the-money).  

So I get the premium regardless of what happens.  From there three things can happen:

* The stock goes up, but not above the strike - this is the "best case" - I made money by owning the stock, and the option expires worthless, so I keep the stock. I made the premium PLUS the amount that the stock went up.
* The stock goes up _past_ the strike price.  I still get the premium, and my stock went up, but I now have to sell it for the strike price.
* The stock goes down.  I lose money on the stock, but I earned the premium from the option, which expires worthless

So a covered call essentially lets you give up some upside for some compensation against downward moves.  Mathematically it's roughly equivalent to selling a put option - you make a little money (from the premium) if the stock goes up but can lose a lot if the stock plummets.