There are two basic types of nuclear reactions: fission - where a big nucleus breaks apart - is relatively easy to trigger, but also leaves behind nasty by products, and requires relatively rare fuels. It's how nuclear power currently works. Fusion - where small nucli are combined - are much cleaner, and use more common fuels but requires very high energies to occur. In other words, the only occur when things are "hot". The reaction itself releases energy, but in practice the ways we use to get the nucli to those high energies are inefficient, so when that's taken into account, the reactor consumes more energy than it release1 . The one exception to this rule is thermonuclear bombs, which don't make good power plants (for obvious reasons).
But what if you could get fusion at lower energies, in other words "cold" fusion? Well, just like with "hot" fusion, you'd have cheap, clean, virtually unlimited power. But we wouldn't need to struggle to find a way to get the nucli to combine at high enough energies efficiently (which has been what's stopped us from developing fusion power in the past). Obviously, this would be a huge discovery. The problem is (and here's the answer to your second question), it simply doesn't work. There have been various people who have claimed to have done it over the years, but none of these claims has turned out to be true. Further, they seem to violate the laws of physics as we know them, so it seems doubtful someone will figure it out in the future.
1 Fusion actually isn't to hard to achieve, if you don't care about generating power. It can be and is done by amateurs.