My understanding of nuclear fission is that some massive isotopes such as uranium-235 are unstable and when split via fission there will be a "slow" neutron. This slow neutron will hit another unstable isotope and this vicious cycle is repeated until you have a chain reaction.
The unstable isotopes are very dense and require high energy to split them - in this case, I would think, ideally a fast neutron. Why does a slow neutron work?
You need slow neutrons because if the neutrons are too "quick" then they scatter of the atoms instead of being captured by them. You can imagine a big lump of playdoh and a much smaller ball of playdoh. If you shoot the small ball with high velocity at the big lump then the ball is scattered - like two billiard balls. But when you put them slowly together by hand they stick nicely together.
If you stay in that analogy then fission looks like this:
You have a lump of playdoh$^{235}$. Now a slow ball of playdoh - let's call it "neutron" - comes along and is captured by the big lump. Since the lump is now bigger by one playdoh unit you have highly unstable playdoh$^{236}$, which then fissions into two smaller lumps. In this process two to three fast neutrons are emitted. Now, since you want the fission to go on you need moderators which slow the neutrons down, or else the neutrons will scatter of the other lumps without combining with them. When you have slowed the neutrons down enough then they can combine with onether playdoh$^{235}$ to form playdoh$^{236}$ etc...
If you're interested it this, then you can play around with this, which I found yesterday: http://blog.nuclearsecrecy.com/misc/criticality/
In the "advanced options" menu there is also the possibility to change the scattering chance. If you set it to 100 percent then you will see that the fission dies down quickly.