An NFL team can have 53 players on its active roster once the season begins. This roster is trimmed from around 100 near the start of training camp at the beginning of August down to the magic number of 53 by Week 1 in early September. The general breakdown of a roster includes roughly 25 offensive players and 25 defensive players with the other 3 being the kicker, punter, and long snapper on special teams.
On the day of a game, an NFL team can activate a maximum of 46 players out of the 53 players on the active roster. These 46 players will almost never be exactly the same for any game the entire season because of injuries, practice squad players being moved to the active roster, transactions, etc.
Every NFL team is allowed to keep a practice squad of a maximum of 10 players. These 10 players can be easily moved up to the active roster in case of injuries or moved back just as easily to move room for returning/new players. However, practice squad players are not protected from other teams who can sign them away from the team they currently are on for their own active roster.
There are 32 teams in the NFL which means that there are 1,696 active players in the NFL with 1,472 being able to play in the games each and every Sunday. The players themselves will fluctuate week to week however these numbers do not. 320 players are also on practice squads making just over 2,000 individuals affiliated with an NFL team at the same time.