I view the length of the crank as mainly tied in to the size of the bike and the rider. The taller the rider and bigger the frame, then the longer the crank arm needs to be to stay in proportion.

You can also use it to vary your RPM. Using a smaller length for the arm means that there is less distance that you need to pedal to make a full revolution. As mentioned, a longer crank will allow you to put more power into each stroke as it has more leverage.

Another way to think of cranks is to compare an ordinary ceiling fan to a giant wind turbine. The fan seems to go really fast, but it also has a short distance to travel to make a full circle. A wind turbine can seem to be going slow, but it can be actually going much faster (and with more force) than the ceiling fan is. It just looks slower and takes longer to make a full circle.