Volume in options is estimated exactly like in stocks. It is defined as the number of contracts which changed hands within a certain time period. The daily volume for example of the call in stock ORCL with strike price $30 and expiration on December 2012 is the number of calls that changed hands in a day. If trader A sold 10 calls to trader B then the volume until now is 10. If trader B sold these calls to trader C then the volume will be 20 no matter if they did it in order to open or close a position.

On the other hand open interest is the number of contracts that are open from the first day the option started trading until now. In other words it denotes the positions that are still open even if they are long or short.

So if someone buys or sells one option to close a position this reduces open interest by one, whereas if someone is making a transaction in order to open a position this increases open interest by one. For example if you buy 20 calls of ORCL to open a long position then open interest is 20. If you sell 15 of them to partially close your position then the open interest is reduced to 5. If you buy again 5 calls to open a position because you changed your mind, then the open interest now is 10 and if you sell these 10 calls to close your long position then open interest becomes 0.