In brief, the job of a Wild Weasel aircraft is to bait enemy anti-aircraft defenses into targeting it with their radars, whereupon the radar waves are traced back to their source so that the Weasel or its teammates can precisely target it for destruction. A simple analogy is that if you're playing tag in the dark, you can shine a flashlight into the night to see where your opponent is, but as soon as you do so, your exact location is revealed, and he or his friends may tag you before you get a chance to tag them.
The Wild Weasel concept was originally proposed in 1965 as a method of countering the increasing North Vietnamese SAM threat, using volunteer crews flying the two-seat F model of the F-100 Super Sabre. However, the F-100F Wild Weasel I, while an effective airframe, had first flown in 1956 and did not have the performance characteristics to survive in the high threat environment.
The Wild Weasel role was then passed in the summer of 1966 to the EF-105F Thunderchief. The F-105 Wild Weasel II was a better platform for this role and was equipped with more advanced radar, jamming equipment, and a heavier armament. The Wild Weasel II F-105F was eventually replaced by the Wild Weasel III variant; 61 F-105F units were upgraded to F-105G specifications.