The most important fact is that Phobos and Deimos are very small. Their gravitational pull is too weak for the moons to pull themselves into spheres.
There are three important facts. The first is that Jupiter rotates very quickly (it rotates once every 10 hours). The second is that Jupiter is composed almost entirely of liquid and gas, making it very easy to deform. Finally, Jupiter is physically very big, which makes the fast rotation have a larger effect. (If you stand far from the center of a merry-go-round, you'll feel a larger outward force than if you stand near the center.)
The debate centers around what provides the energy source for the belt-zone circulation. One theory says that energy deposited in the upper part of the atmosphere by the Sun provides the energy. Another theory holds that the energy is provided by the flow patterns deep inside the planet.
Io has no craters because it has many active volcanos which resurface the moon very quickly.
Europa's surface is ice, which is much easier to melt than rock. Therefore it requires less energy to melt Europa's surface and erase the craters than it does for a typical rocky moon.
To correct a common misconception: Europa is not younger than Io, Callisto, or Ganymede! When the text refers to Europa as ``youthful,'' it's talking about Europa's surface, not the moon itself.
Studies of the tides Jupiter raises on Europa led to the conclusion that Europa may have a liquid water ocean hidden beneath it's icy surface.
Some people speculate that geologic activity on Europa could provide the energy needed to sustain bacterial life in the layer of water.
One way to study study Europa's ocean it to simply send a probe that will melt its way through the ice and directly study the ocean beneath.
There's lots of information available about Cassini at:
http://saturn.jpl.nasa.gov/cassini/index.shtml