Ajax is an industry buzz word that refers to many different effects found on modern web sites today. Specifically, Ajax techniques allow web pages to update specfic sections of itself without needing to refresh the entire page. This means that your website will respond faster and can respond more like a typical desktop application.
It allows web pages to load much quicker because there is much less data being trasferred at any given time. This also means that you save valuable money on bandwidth because your server isn't sending out as much data.
Ajax also refers to animation effects that we see on many web sites today. Typically Ajax enabled web sites can provide nice graphical animations that we used to only find in Flash-based web sites.