What happens
Diffusion is the net spreading of particles from regions of higher concentration toward regions of lower concentration, even though individual particles move in many directions.
The process is usually faster over short distances and at higher temperatures. In liquids and gases, molecular motion can gradually erase a concentration difference.
What changes the process
A drop of dye spreading through still water is a useful picture, but real mixing can also involve convection. Diffusion itself does not require a bulk flow of the fluid.
Why it matters
Diffusion matters in cells, membranes, gases, alloys and countless chemical processes. At microscopic scales it is one of the basic ways matter redistributes itself.