The reason some leagues like to incorporate waiver wire rules for free agent players is to create parity in the league. Basically, it gives teams two things: time and priority.
Generally the waiver priority order is set by reversing the draft order. It gives priority to the team with that began with the biggest disadvantage, the team with the last pick. The advantage to being at the top of the waiver order is that a free agent is considered on waivers for a certain amount of time. Team owners can claim the player on waivers, but the transaction will not be processed until the waiver time has elapsed. If more than one owner claimed the player on waivers, priority is given to the owner at the top of the waiver order and the player goes to that owner. The waiver order is then changed, with the owner who successfully picked up the free agent moved to the end of the list, and everyone else being bumped up one spot.
This system ensures that owners don’t simply get beat to the punch for picking up valuable free agents. Once a free agent clears waivers, meaning that the amount of time given to all owners has elapsed, all claims to that player are immediate and do not effect the waiver priority order.
This is one of the hardest concepts new fantasy players have to grasp about leagues that incorporate waiver rules. Many veteran players don’t really understand why waivers are in place or how to use them effectively. A waiver wire strategy would be one where the owner takes into account the probability that a player will clear waivers, ie: Does anyone else in the league even want to pick up this player? If not, then it is pointless for an owner to damage their waiver priority, and they should just wait for the player to clear waivers.
Equally important is to read the leagues waiver rules. They can be VERY different. For instance: After the draft in a league I play in I decided to drop the defense I drafted and pick up a defense with a better week 1 matchup. I didn’t realize that this league’s waiver rules began before week 1 of the season, and I had picked up that defense using my waiver priority. I was then dropped to the end of the waiver priority order. If I was smart enough to read to rules before hand, I would not have wasted my waiver priority on a defense with a better matchup. I’d much rather have used it this week to pick up the new Patriots QB. That seems unlikely now since I am dead last in waiver priority.