I remember this being a minor fad around this when I had my first, handcoded website hosted on the 5MB of webspace my dial-up ISP gave me. I'm pretty sure I heard about it from one of the other regulars on irc.scifi.com, the Sci-Fi Channel's IRC server that I used to frequent.

With a little cut-and-paste of some code from Swatch's website you could have a GIF 'clock' on your site that showed the 'internet time' to your visitors. Utterly pointless, but harmless fun.