There are many different ways things could implode. An implosion is simply the opposite of an explosion. In an explosion, matter and energy fly outward, but in an implosion, matter and energy collapse inward. All implosions will need some sort of pressure from the outside pushing in to cause the object to collapse. So in short, implosions are caused by having a greater pressure on the outside of an object than on the inside.

One easy situation to think about would be a submarine. There's a whole bunch of water surrounding the submarine, and it's pushing in on the metal hull, trying to get inside. This is because water is much more dense than the air inside the submarine, so it has a much greater pressure. The metal that makes up the submarine is very strong, and made in such a way to keep the water out. But if part of it breaks, the water will rush in, and if it tries to rush in quickly enough, it will make the submarine collapse, or implode.

You can actually do an experiment like this right in your kitchen. If you fill a metal soda can with a little bit of water and place it on the stove, it will heat up the water, causing it to boil into steam. If you quickly (and carefully, since it's very hot!) flip the can over and place it in some ice water with the opening at the bottom, it will implode. This happens because the cool ice water causes the hot steam inside to condense into water. Since the water is much more dense than the steam, there's much less pressure inside the can all of the sudden, and the outside air pressure is enough to cause the can to implode.

There's another cool way to cause an implosion. Nuclear bombs explode when unstable material reaches a certain critical density. In order to make the material dense enough to explode when the bomb is detonated, smaller explosions occur all around the outside of the material. All these little explosions push inward on the material in the center, causing it to implode. Once that happens, the nuclear reaction can now take place, and the bomb goes off.