Nuclear fusion takes place when 2 smaller atoms are smashed together and form a bigger atom. Again the bigger atom weighs less than the original 2 smaller atoms together and the difference in weight is turned into pure energy. The waste produced in this process in not that radioactive, so that is a big advantage. The problems is that the process can only take place at very, very hot temperatures. Think the center of the sun and you will be about right. Nuclear fission is actually the power source of the sun. So far we haven’t been able to control these high temperatures, but there is a solution.
Helium-3 can be used to get nuclear fusion going at lower temperatures that are manageable. The problem is that it can’t be found on earth. On the moon however it is widely available and it is economically viable to mine it and transport it back to earth. The Russians plan to start doing this in 2015 and NASA wants to have a permanent moon base by 2024.