I call these kinds of lenses "pumpers" because the physical extension of the lens tend to make a suction effect and it sucks air in or out.
in optical terms, "breathing" is used to describe "focus breathing" as was stated above so the correct term should be "suction" and I will use suction from now.
lenses that extend quite a bit (doesn't matter if it's manual or autofocus lenses) will create space inside the lens barrel as it extends and that space has to be filled by air. when a lens sucks in air, it brings dust and pollen into it (and fungus spores). this is inevitable. you can demonstrate this yourself by getting a lens that extends a lot and placing the end of it close to your eye. extend and retract the lens and you will feel a very slight air current.
that current gets stronger as you pump the lens faster.
some lenses will have less tendency of doing this when they have a fixed rear element (but air still gets sucked in), or when the lens has a fixed dimension as you zoom in or focus such as the (70-200 family of lenses). since the lens is "sealed" like the case of the 70-200 lenses, not much air is getting sucked or pumped.
there are times when the current is so strong that you can feel it from the eyepiece of the camera. this happens with older or cheaper cameras and this is what ken rockwell calls "eyeblow".
if you really want to see this visually, blow some smoke from a cigarette and then pump your lens and you will see the smoke go in or out of it. I shoot clubs before and I see this sometimes. I know, this is not very smart but it can't be helped. there are lenses with gaskets and felt seals that help filter dirt and stuff but some junk still manage to get through.
hope I made sense.