*sigh* Time to explain everything again.
Ok, so EUD stands for "Extended Unit Deaths". It was a method of minipulating starcraft's triggers to overflow, and manipulate the memory. Because of the nature in which it manipulates memory, EUD only works on computers running windows.
EUD actions could actually manipulate starcraft's memory in game, this allowed map makers to do basically mod SC in game. However, some people discovered that with certain triggers, it was possible to manipulate the memory outside of SC. This means that theoretically (although I doupt it would ever be done), SC maps could be used to steal information from others, or install malicious programs onto other people's computers. It was very important that blizzard patch this Because if they didn't, being a major corporation, they could get sued for a lot of money, if any kind of business could demonstrate that one of blizzard's programs was responsible for damage to the buissness's operation,
EUD conditions are less powerful, they can detect starcraft's memory in game. So while EUD actions could set the current health of a certain unit, EUD conditions could detect the health of that unit.
After EUD, EAS, and ESS were discovered. They were different methods of doing the same thing, but blizzard patched those as well.
Heim created an EUD enabler, that got around blizzard's patch by modifying the starcraft memory after battle.net had preformed it's checksum. However, a rumor got around (I'm not sure how much of it was true) that people were getting banned for using the EUD enabler, and Yoshi was attempting to seek offical support from blizzard at the time, so the EUD enabler was taken of the site. Since then EUD enabler, like most memory patching programs, needs to be upgraded everytime a new patch comes out, it no longer works on battlenet, and Heim has decided not to update it, and has moved on to a secret project (which he's never going to finish in my opinion).
The thread in which DeathKnight discovered EUDs A concept map, where EUD conditions are used to "utilize the arrow keys" A map, made by me which utilizes EUD conditions to "detect where you click"