So, each week there is a Thursday Night game which is broadcast nationally on free-to-air television (for the first 10 weeks, the last 6 weeks are on cable, unless it's a local team, then it's free to air)
The two networks that carry the games, CBS and Fox, show 1 or 2 games each Sunday, depending on the week (for example, Week 1 Fox will show 2 games and CBS will show 1, Week 2 Fox will show 1 game, CBS will show 2, etc...). These games are based on regional zones by "primary" and "secondary" markets. Regardless of where your team is playing, if you live in the "primary" zone, you will see your team play every week for free (unless it's on Monday Night Football, which is on the cable channel ESPN).
There is also a Sunday night game, which is nationally broadcast, and then Monday Night Football, which is nationally on cable (ESPN).
So, for example, if the Patriots were playing at 4:25PM on a Sunday, the residents of their primary area (which is all of New England) will get two games to watch at 1 PM, and then their team at 4:25 PM. However, if the Patriots play on Thursday Night, Sunday Night, or Monday Night, New England still sees three games every Sunday afternoon.
And if that's still confusing, here's a wikipedia page on just this subject:
https://en.wikipedia.org/wiki/National_Football_League_on_television