There are 32 teams in the NFL, each consisting of 53 players on their roster, plus members who are also on injured reserve and some scattered lists. What this all adds up to is roughly 1700 players active and eligible to play on Sundays at any given time.
Every year, the NFL drafts over 250 college rookies, and signs another few hundred players as college free agents. This pool of 600-plus players accounts for hundreds of roster spots around the league every year, replacing players who were on rosters the year before, even accounting for players who choose to retire.