To understand fusion you have to understand fission.
Regular nuclear power is provided by fissile materials such as uranium. When struck by a high energy particle, this happens:
Basically when a neutron strikes a uranium nucleus, this causes the nucleus to split into it's component parts: protons, neutrons, and electrons. The protons and neutrons dissipate, whereas the neutrons continue on to strike other uranium nuclei, causing further reactions. This is a nuclear fission chain reaction.
Why is this useful for creating power? Because every time you split a uranium atom, a bit of heat and light is produced (mostly heat). When you have hundreds upon thousands upon hundreds of thousands of uranium nuclei splitting, you can produce a pretty damn good amount of power. This is transferred into a water pipe running through the system which turns the water into steam, which is under high pressure, and is then used to drive a turbine which drives an electric generator, producing power.
If you have enough uranium and strike it with a neutron, then one atom will split, producing more neutrons, which will then make it's neighbors split, who will make THEIR neighbors split... This is why it is referred to as a chain reaction, as one atom splitting will send a wave of splitting atoms across the whole material until there are no uranium atoms left.
A nuclear bomb uses this principle to build up a massive amount of heat and pressure from a completely uncontrolled nuclear chain reaction inside a heavy metal casing, until said casing ruptures and detonates.
In a regular nuclear reactor, the reactor itself would become so hot it would melt through it's own containment and into the ground (a "meltdown"), not explode. It's functionally impossible for a nuclear reactor to become an atom bomb.
A runaway fissile reaction is dangerous, but there are multiple methods to control it, the main one being control rods. These are inserted into the fissile material to slow down or even stop the reaction, and are used to prevent it from becoming a runaway one. If handled improperly, however, as it was at Chernobyl, a meltdown situation could occur. Chernobyl was mainly an issue with the reaction containment rupturing along with the coolant towers, releasing radioactive material over a wide area. It wasn't a nuclear blast, it was a meltdown.
Now, I've covered fission, so why is that important? Well, fusion is the same deal, except instead of splitting the atom, we're joining two atoms together.
http://upload.wikimedia.org/wikipedia/commons/3/3b/Deuterium-tritium_fusion.svgYou can do this in a variety of ways, but the most economical is probably the method pictured above - a fusion of two different hydrogen isotopes, deuterium and tritium (hydrogen-2 and hydrogen-3, respectively) to create a stable element, helium-4. This produces one extra neutron and a small amount of heat and light.
Why is this so important? Well, a number of reasons.
1. Each individual fusion reaction produces about quadruple (IIRC) the energy of a single fusion reaction. This means you can get four times the power with fusion.
2. There is no possibility of a runaway fusion reaction, for reasons I am going to cover in a moment.
3. It produces helium-4, which to my knowledge is not unstable, will not decay, and is not considered nuclear waste.
4. No pollution whatsoever, as helium-4 is not a greenhouse gas.
5. Highly economical. The only materials you need once the reactor is built are deuterium and tritum, both of which are easy to get one's hands on (the oceans are FULL of hydrogen)
6. The only radiation it produces is alpha radiation (which is, in actual fact, a helium-4 molecule moving at a high rate of speed) which is so weak it can be easily stopped by a piece of paper.
Why is there no possibility of a runaway fusion reaction?
Because fusion reactions are not chain reactions.
Splitting a uranium atom will cause all of it's neighbors to split.
However, fusing deuterium and tritium will not cause other deuterium and tritium to fuse. This means you don't need control rods or mechanisms of any sort - you just have to turn off the device, and the reactions will stop themselves, without any need for additional input. It's not a chain reaction, thus, it can't meltdown unless somebody leans on the "ON" switch for a few hours.
If it's so good and clean and simple, why are we not using it already?
Because... well, as one researcher put it "We're going to put the sun in a box. However, we don't know how to build the box."
Basically the problem is this. It takes a LOT of energy to force deuterium and tritium to fuse. The best way to do this is to smash them into each other as hard as possible (think a particle accelerator). However, doing just one collision will not cut it. You need to smash a huge amount of them together all at once and then find some way to keep doing it over and over and over and use the resultant heat for power generation.
The good news? Deuterium and tritium can be accelerated, and then controlled, by magnetic fields. This means that we already know the principles that will allow us to make the box.
The bad news? A fusion reactor takes a LOOONG time to build, and is very expensive. And we're still not sure which of the many methods proposed will give us the most benefit, so we have to build them all to see which one works the best.
The main reason we don't know how to make the box is, well, we don't know which of these will give us the best bang for our buck or even cost effectiveness (as in we need to produce enough power for the thing to be worthwhile). There are all sorts of proposed designs that nobody has ever tested:
The Tokamak, a russion design that is basically a large particle accelerator arranged in a torus (doughnut) shape? (This one seems like the most likely)
http://upload.wikimedia.org/wikipedia/commons/2/2b/NOVA_laser.jpg (It's a URL as it's a large image)
Instead of magnetic confinement, could we use lasers?
Or hell, maybe we could use this old thing from the 1960s. Who knows? Not me.
