Imagine you have two balls. These balls really don't want to touch each other but if you put a lot of energy into forcing them to, they explode releasing tons of energy.
This is called nuclear fusion. The balls are certain atoms and the energy is usually extremely high temperatures(millions of degrees). Instead of making the two atoms touch you are combining them into one larger atom. This process is what the sun is doing to create all of its energy.
Cold fusion is the term for a Nuclear Fusion reaction that can be done at a relatively cooler temperature and other conditions that we can create on earth. Although currently there is no cold fusion technique that produces more energy than what is required to sustain the reaction, Emc2 is currently working on a Polywell fusor that seems to produce more energy than it consumes. It is currently being funded by the Navy.
I'm pretty sure, though, that they wouldn't want to be associated with the term cold fusion, owing to its pseudoscientific stigma.