mDNS (aka zeroconf, Rendezvous, and Bonjour) is a way for devices to advertise the services they have on the network. A computer still needs to support that service (with the appropriate drivers) in order for them to use the service. For instance, if you had Macs on the network, they would see the HP 2300dtn on the network and allow you to select it as a printer; then the Mac would download drivers and install them automatically.
Airprint is built on Bonjour, so that it allows you to find printers. But it also goes further by letting you print without needing any drivers. The protocol hasn't been published (that I can find) but apparently it normally spits out fairly standard formats (JPEG and PDF) that printers can understand.
There are various ways to enable desktop computers to advertise Airprint for other devices. The Wikipedia article on AirPrint mentions software for various platforms that can enable it. If you are using CUPS, versions 1.4.6 and greater automatically support AirPrint.