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This parameter adds extra particles around the simulated particles. This way, a much lighter simulation with a small amount of particles can produce a more dense cloud by multiplying them at render time. The new particles are affected by the speed of the original ones, so your particles must have some velocity speed or this parameter won't have any influence. Note that more RAM will not be used if you create extra particles, this depends again on the final number of cells created by the cell size parameter. If you do use a high dispersion though, it is likely that many more cells will be created since the total bounding box of the particle cloud will increase, thus increasing the amount of RAM needed for rendering.
Extra particles set to 0, 10, 200. Dispersion was set to 0.1 (10cm) in this case. RAM usage only very slightly increased even with 200 extra particles per particle. The right most image shows the particle radius increased to avoid seeing the individual particles.
Extra particles dispersion
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