There are two main forms of nuclear energy, fission, which involves splitting atoms apart, and fusion, which involves releasing energy when 2 atomic nuclei are forced close together and fuse into a single nucleus. Fusion, which is the method by which stars generate energy, is more efficient than fission and does not produce radioactive waste. This means that scientists have, for several decades, been trying to find a way to harness fusion as an energy source. Unfortunately, the amount of energy needed to create fusion reactions and the high temperatures and energy requirements for it, have meant that fusion has not been an economically viable source of power.
Cold fusion is a concept of using chemical reaction to create fusion at room temperatures. In 1989, Fleischmann and Pons claimed to have achieved this, but their claims were disproved in short order. As of 2016, a few scientists are continuing to work in this area, but their work is still exploratory and at this point there have been no experiments which demonstrate that cold fusion actually happens. Thus at this point, one can say that although cold fusion is an interesting concept, there is no evidence that it is actually possible with current technology much less a viable source of power.