From the name, I thought dispersion forces would be repelling or dispersive forces between atoms, and not attractive forces. What is the dispersion part of the name actually referring to? Is it the electrons moving around?
Although Danny Rodriguez has already excellently exposed what the dispersion force is in simple terms, the word dispersion still demands a better explanation in my opinion.
According to Wikipedia:
The London theory has much similarity to the quantum mechanical theory of light dispersion, which is why London coined the phrase "dispersion effect." In physics, the term "dispersion" describes the variation of a quantity with frequency, which is the fluctuation of the electrons in the case of the London dispersion.
So the word "dispersion" here is a mere analogy. The original work is this one (in German).
It refers to the electrons that are distributed (or dispersed) in the electron cloud which then ensues an attraction between atoms or molecules.
Electrons can be dispersed in any number of different ways in an electron cloud. One way, however, is where all the electrons appear in one side of the electron cloud. When this polarization happens, the atom has a negative charge on one side (where the electrons have gathered) and a positive charge on the other side.
This induces neighboring atoms to polarize the same and therefore attract to each other in a negative-positive-negative-positive chain.
A good example would be helium.