Nuclear fusion is when lighter elements like hydrogen, helium and lithium fuse together to form heavier elements. This will release a huge amount of energy far more then any chemical reaction.
However to get nuclear fusion you need to overcome very strong repulsive forces between the atoms. For example the entire weight of the planet Jupiter is not enough to start fusion.
The weight of the Sun is however enough to do this. So the atoms at the core of the Sun gets pushed together with enough force that they fuse together releasing a lot of energy in the form of heat and light. That is what powers the Sun.
Making this happen continuously in a stable environment for a power plant is a lot harder though. But we have very recently found out how to do this using lasers and magnets instead of nuclear bombs.
The leading effort of acheiving fusion is at Lawrence Livermore National Ignition Facility, and involves 156 of the largest most powerful lasers ever made.
They all concentrate on a single point. At this point, they will suspend a pellet, I forget what the shell is made of.
Inside, the pellet is full of deuterium and tritium, hydrogen isotopes. The lasers will suspend the pellet, burn the shell off, and then crush and superheat the isotopes.
We can’t acheive the pressures found in the core of the sun, but we can exceed the temperatures, which, on paper, is just as good.
Recently it was reported that there was a breakthrough, where the facility heated and compressed a capsule of hydrogen to previously unattainable temperatures and pressures, igniting fusion reactions that produced 50% more energy than the laser beams had delivered.