What would cause a central air conditioner to make a dripping sound in the inside unit and leak water?

When air is cooled the water in it comes out (like mist forming on the outside of a class filled with cold coke) and this happens in the air conditioner. Normally the dripping water is drained way to the outside (or a drain) by a pipe. If the pipe gets blocked the water will overflow and the conditioner will leak water - get it serviced.