GDC ... Game Developers Conference; this is a conference that spans 4 days that is for developers to show new technologies or explain how to make the most of current technologies.
Think of it as School for Game Developers, it has actually nothing to do with games specifically.
Siggraph ... Computer Technology Conference; identical to GDC in many respects, difference being it covers the entire spectrum of anything computer based rather than just game technologies.
E3/ECTS ... Electronic Entertainment Exposition/European Computer Trade Show; these are for developers to go "check it out! my game has better graphics than everything... but you can't play it for like 2years yet cause were no where near finished."
There are a few more events each year but those are the most important. Oddly E3 has moved back again, it was originally set for next week (as it traditionally is); however somewho it moved back 2weeks to April, then a month ago it moved even further back to May.
So a quick sum up for those with minute attention spans.
GDC = Game Technologies (for developers only)
Siggraph = Computer Technology/Theories (for computer scientists only)
E3/ECTS = Game Showcase (for developers to make the public drool)
Athlon64 FX-51 | 1.5Gb DDR2 PC3400 | GeForce FX 5900 Ultra 56.60 | DirectX9.1 SDK | Audigy2 | Windows XP 64-Bit