If an NFL team has hired a new head coach this year, it can start its offseason program on Monday. For teams that don't have new head coaches, the offseason program begins two weeks from Monday. The offseason program is basically a series of workouts during which players can finally start talking football with the teams. Until the offseason program, players can't talk about football with their coaches.
This means the teams who hired a new head coach this offseason have officially started their offseason program. Interim head coaches who were then hired to the fulltime job, like the Chiefs' Romeo Crennel, do not count as new head coaches, so their offseason program doesn't start for two weeks.
If your team has hired a new head coach, it's usually (but not always) because the last one failed, so this is the NFL's effort to smooth the transition for those new head coaches.