In the NFL, one key aspect of contract negotiations is guaranteed money. A player’s salary for a given season of a contract is not guaranteed unless specified in the deal. That is the reason you hear that teams save money against the salary cap by cutting players during the offseason. The team isn’t on the hook for the salary.
That changes with Week 1 of the NFL season. Vested veterans have their contracts fully guaranteed for the year if they are on a Week 1 roster. A vested veteran is a player with at least four years of experience.
For a lot of players, this is an academic exercise. Some veterans are never in any danger of being cut, but it can be a big deal for those players who are barely hanging on. A spot on a Week 1 roster increases the odds of that player sticking for the entire season. It also obviously guarantees a player his money even if he is cut.
You might see a relative flood of veteran signings between Weeks 1 and 2 as a result. Contracts for veterans are not fully guaranteed if a veteran joins a roster after Week 1. There are some guarantees, either 25% of the salary or one extra week of pay, whichever is more, but this is far greater flexibility for the team.