2G is the current generation of mobile phones. It transmits sounds primarily, in digital form, over a circuit-switched network. Data service is possible, but only via circuit switching.
3G was supposed to be the next (third) generation of mobile phones. It is packet-switched (more efficient, faster) rather than circuit-switched (less efficient, slower), and can transmit data (e.g. pictures, movies, etc...) as well as voice. But, by and large, it requires a different infrastructure than 2G. Due to cost and complexity, rollout of 3G has been somewhat slower than anticipated.