Offenses have a wide variety of formations and feature a lot of different skill players. On defense, likewise, there are a lot of formations and have some of the best players on the football team. There’s an old saying "Offense wins you football games, defense wins you championships."
Defense is an extremely important part of a football team. Defenses are called by the number of down linemen and linebackers they have. For example, a 4-3 has four down linemen (players who are in a "down" position playing at the line of scrimmage) and three linebackers (players playing 3-5 yards off the line of scrimmage). A 5-2 has five down linemen and 2 linebackers, and so on.
Most defensives use a 4-3 scheme, so we will focus on that, though the other defenses just add or subtract a player here or there, so the formations are generally the same with a different set of players. In a 4-3 defense, you have four down linemen. On each end of the line, you have a "defensive end" who contains the outside. This means he doesn’t allow any plays to come outside of him. If they are sweeping his side or reversing and running to his side, he is always focused on tackling the ball carrier or forcing the play back inside where he has help.
The two interior linemen focus on stopping the run and pressuring the QB on passes.
The three linebackers have a lot of responsibility. You may have heard the nicknames "Sam", "Mike", and "Will". The Sam linebacker is the Strongside linebacker. The Mike linebacker is the Middle linebacker and the Will linebacker is the Weakside linebacker. Strongside is the side where the most players are. For example, if you have a wide receiver on each side of the offense and a tight end on the defensive left side, it is a strong left. The linebackers have responsibility for the run and the pass if it is in the area they "cover".
Covering the wide receivers are the cornerbacks, also called the defensive backs (DBs). The DBs have pass coverage responsibility. Depending on the defense called, they have responsibility for either covering a specific man (not letting him catch the ball) or covering a specific "area" of the field – not allowing any player in that area to catch the ball.
In the back of the defense are the safeties. The Safeties try to not allow any play get behind them. The Strong safety lines up on the strong side and has both run support (tackle the running back) and pass support (tackle the receiver or prevent them from catching the ball). The free safety is primarily responsible for making sure no receiver gets behind him and makes a play. When we say the defensive backs and safeties try to prevent a receiver from catching the ball, there are certain rules they must follow. They cannot "interfere" with the player, though they have an equal right to go after the ball as the receiver does.
The 4-3 is a typical defense you will see this year.