A radiator is part of a water cooled system. this is the one I have:
instead of a fan over the cpu heatsink there is a pump that pumps water around a closed loop to the radiator, where the heat from the water is exhausted to be sent back to the CPU heatsink.
A standard cooler is like this:
just a fan above the heatsink.
So which is better? well there are lots of arguments for and against so I wont get too far into it now. I personally prefer liquid cooled, its nice and quiet and takes the heat out of the CPU area better, downside is it doesn't cool the CPU socket as well.
Another point is that you only need an aftermarket cooler if you are going to overclock your CPU. if you are not going to overclock, it will come with a standard cooler (a bit like the 2nd image) that has no radiator and this will do fine.