Waivers in fantasy football are a claim. The waiver wire is a pool of free agents available to add to your team. You use a waiver to make a claim on a player in the free agent pool. Whenever waivers are processed (usually at the beginning of a respective week), that player is added to your team.
Once a team drops a player, they go onto waivers before becoming a free agent.
PRO TIP: If more than one owner makes a claim on a player, the team with the highest priority will receive the player when the transaction is processed. Most leagues have a system in which the more acquisitions you make, the lower your priority is in claiming future players.
Waiver hawks are team owners who are constantly adding players to their team via the waiver wire. This is a very risky strategy in fantasy football as you could end up with weaker players than what you may have started with.
Free agency is a system in which players who are currently not on a team are available to acquire, assuming that all of the roster spots on the team are not full. Its valuable asset when trying to improve your team after an injury or a weak performance from a player, or maybe to fill a starting spot during a bye week.
A crucial part about adding free agents is looking at their current matchup. Since many free agents are just replacement players, it is important to consider whether they have the optimal chance to perform while on your roster.