ICEAuthority http://serverfault.com/questions/119580/what-is-iceauthority-file-in-opensuse-11-2
Here is a good paper on what ICE is, and what it does.
Basically ICE is a inter process communication protocol, with authentication, protocol negotiation and potentially multiplexing built in.
It allows two X clients to talk directly to each other, for example, a video player program could potentially talk to a jukebox program to update each other.
As Richard Holloway says, the .ICEAuthority file is for authentication. It contains a number of random cookies.