Open Interest is a count of how many option contracts exist for the specific combination of underlying stock, expiration, and strike price.
More open interest is better, because it means there is more liquidity for the call option you are trading. More liqudity means smaller spreads between the bid and ask (which is good for you, should you ever need to close out a position before expiration).
In general, you should stick to writing calls that have an open interest of 1000 or more (which is the default value of our Open Interest filter -- we're looking out for you!).
How It Works (in case you're curious; you don't need to know this)
Option contracts are different than shares of stock in the sense that there is no fixed number of option contracts. There could be zero, or there could be many thousands. New option contracts are created every day.
In the beginning, when a new call option series starts trading the open interest is, by definition, zero. No options of that type exist yet. If one person sells 5 contracts and someone else buys 5 contracts then open interest is 5, meaning that there are 5 such contracts in existence. If another person sells 2 more (and someone buys them) then the open interest increases to 7. There is no upper limit to how many can be created/sold (as long as there are buyers).
At some point the sellers of these contracts may buy them back (thus reducing open interest) or at expiration two things could happen: the options are out of the money and expire worthless, or the options are in the money and will be exercised. In either case, the open interest for that series will drop to zero on the day after expiration.
Note that the definition of open interest is not the same as volume. Option volume tells you the total number of contracts bought and sold, but if some of those purchases or sales were closing transactions, then the volume will not be the same as the open interest. A closing transaction will reduce open interest but increase volume.
All you really need to remember is that you should probably stick to selling options that have an open interest of 1000 or more. That will keep you in fairly liquid options that should have reasonably tight spreads.