right, media are just the stuff you put in your filter, as sarcare said.
It can be mechanical filter media, like the white cottony stuff used to trap floating crap. It can also be chemical filter media, like carbon. The most important kind of filter media is probaby biological. This is a high-surface area place for bacteria to live. It is usually BioFoam or some kind of cell pore media (whether a block, or rings, or stars).
In my tanks, I have stopped using chemical filtration. There's no need for it as I do frequent water changes, and carbon removes nutrients needed by my live plants. So the two I use are biological, and mechanical. Make sure the mechanical media is first (e.g. water has to go through it before the biological media), otherwise crap will clog the Bio media and suffocate the bacteria. The good nitrifying bacteria require oxygen to do their job, which is usually provided by clean water and good flow.
As DeRo said, you can also get fancy with filter media and use ones that will change your water chemistry (safely and minorly) to get desired qualities like higher hardness or lower pH. I guess these might fall into the chemical filtration category, but peat and crushed coral are much safer to use than straight-up chemical pads and resins, because they're natural.
As stated, you don't need an air pump. Most advanced aquarists don't use them because they understand the need for good filtration and lots of circulation. Surface agitation is the most important thing for oxygenating your water. In fact, that's mostly what an air pump does, is increase surface agitation.
hope that helps!
