The basic idea is that every week, you have the opportunity to 'draft' a player(s) who was unchosen. The rules vary from league to league, but might go like this:
During week 3, Aaron Rogers gets hurt. His backup, Flynn finishes the game throwing for 300 yards and 3 TDs. Team A has Rogers, and no one drafted Flynn. The medical report says Rogers is done for the year. Team A thinks Flynn will make a great backup, so he puts in a waiver wire request to pick up Flynn, and 'drop' Rogers from his team. However, team B is weak at QB- he drafted Cutler, who so far is having a terrible year. He too, puts in a waiver request for Flynn, and to 'drop' Cutler. According to the League Rules, each week the waiver wire resets to the reverse order of the standings- that is, the worst team gets first choice. In this case, Team A is 2-1 and Team B is 1-2. Team B is granted his request for Flynn. Flynn is now a member of his team, and Cutler goes back into the player pool. Now team A is still without a QB. (a smart owner would have put in a 2nd request for another choice, in case someone snatched his first choice). He must put in another request for a different QB.
Rules vary as to how the waiver order is determined each week, when the waiver wire is 'open', and how many days you have to wait before picking up a player that was dropped (for example above, when Cutler was dropped- Team A couldn't just pick up Cutler right then- the rules usually say when a player is dropped, he is 'on waivers' for a minimum of 2 days to allow other players the opportunity to see that he is on waivers and put in a request. Now that you know the basics- you can re-read your league rules and hopefully understand how your league handles the wire.
Hope that helps. Good Luck!
I drink because of the 1998 NFC championship game.
12 team big $$$ non PPR league - QB RB RB WR WR TE D K
RB: Murray, Matthews, R.Bush, D. Brown
WR: Julio Jones, Colston, VJax, Garcon
TE: Witten, Gresham