Can you help me to better understand?
Teams are limited to 53 active players, right?
To my understanding, you can now have 55 men on the roster of which 48 are eligible to play.
Are teams permitted to have additional players that aren't on the 53-man roster?
There is also a "practice squad" of 16 players. These are players who have limited time in the league, although the rules have changed over the past few years so a lot more players are eligible now than just a few years ago.
When a player is on the practice squad, they practice with the team, but aren't eligible to play in games unless they get "activated" and moved up to the active roster a number of days before the game. (I'm not sure offhand of how long that is.) This is a way to stash players who are good but just need more work to develop.
When players are cut or waived, they can be re-signed to the practice squad if they meet the eligilibity requirements.
Players on a practice squad can be "activated" and signed to the active roster of ANY team in the league. So good players can be poached at any time.
Texan's Great Arian Foster started his rookie season on the practice squad and wasn't activated until the end of the season. It can be a way to develop raw players. Steeler Great James Harrison spent a couple of seasons on the practice squad before he blossomed and became a monster.
You can also put a player to the injured reserve. If you put a player on the injured reserve, they don't count against your active roster. They're still on your team and you're still paying them, but they don't play or practice. It used to be that when you went on reserve, you were out for the rest of the year, but there have been recent rule changes that allow players to be brought back onto the active roster from injured reserve in certain cases.
Approximately how many players will be competing for spots with the Texans this summer?
If I remember correctly, and if they haven't changed it, training camp would start with up to 90 players. During the pre-season, there used to be multiple cut-downs, but I think they've changed that so that there's only one cut down (maybe two) to get down to 53.