As in heat transfer there is a convective (flow-related) mode and a diffusive (conduction-like) mode.
Diffusion is the transfer of mass due to random molecular motion
The actual origin of diffusion is actually relatively easy to follow. Consider a box that (for some reason) has a high concentration of dark particles on the right and a high concentration of light particles on the right. If the particles are randomly jiggling around (which we know they will since they are at a temperature higher than 0 K), every now and then one will cross the center line (for simplicity, let's assume that two always cross at the same time, one going right and one going left, so that the overall concentration doesn't change).
If one of these "swapping" events occurs, it is quite likely (given the original concentrations) that it will move a light colored one from right to left and a dark colored one from left to right, causing a net flow of light particles from right to left and a net flow of dark ones from left to right. This same idea will hold true until both sides are at the same concentration. At which point swapping will not change the concentrations on either side (on average).
Convection refers to the transfer of mass due to an externally imposed flow.
This definition is slightly different than the convection in heat transfer because the flow here must be forced (there is no analog of "natural" convection for mass transfer -- although we will see something slightly like it later).
Describe the primary modes of mass transfer