Bonjour is Apple's implementation of set of techniques which allow for a zero-configuration IP based network. It comes standard with Mac OS X, and mDNSResponder.exe is the Windows port/version.
In laymens terms, that translates to a simple setup of devices on a network which "just work" without the need of specialised servers or configuration. It makes it easier to find printers, other computers, share files, etc.
The service runs in the background broadcasting your networking information so other devices (such as printers) can respond if they offer a service you may require.
I've noticed it bundled in installers such as Adobe Photoshop, Skype and iTunes.
The annoying thing is theres no uninstallation option for it!
For me, being the sort that likes to set things up myself, I don't need it.
And it is annoying having another application running unecessarily in the background.
To remove Bonjour, follow the steps below:
1. Open command prompt.
2. Type: "cd %PROGRAMFILES%\Bonjour"
3. Type: "mDNSResponder.exe -remove"
4. Type: "rename mdnsNSP.dll mdnsNSP_old.dll"
5. Restart your computer.
6. Once Windows has rebooted, delete that folder and its contents.
ProcessLibrary, Raymond.cc, Wikipedia