The 4-3 defense
Tom Landry invented the now-popular "4-3 Defense", while serving as Giants defensive coordinator. It was called "4-3" because it featured four down lineman (two ends and two defensive tackles on either side of the offensive center) and three linebackers — middle, left, and right. The innovation was the middle linebacker. Previously, a lineman was placed over the center. But Landry had this person stand up and move back two yards. The Giants' middle linebacker was the legendary Sam Huff.
Landry also invented and popularized the use of keys — analyzing offensive tendencies — to determine what the offense might do.
When Landry was hired by the Dallas Cowboys he became concerned with then-Green Bay Packers Coach Vince Lombardi's "Run to Daylight" idea, where the running back went to an open space, rather than a specific assigned hole.
Landry reasoned that the best counter was to take away daylight.
The "FLEX"
To do this, he refined the 4-3 defense by moving two of the four lineman off the line of scrimmage one yard and varied which line people did this based on where the Cowboys thought the offense might run.
This change was called "The Flex Defense" because it altered its alignment to counter what the offense might do. Thus, there were three such Flex Defenses — strong, weak, and "tackle" — where both defensive tackles were off the line of scrimmage. The idea with the flexed linemen was to improve pursuit angles to stop the Green Bay Sweep — a popular play of the 1960s.
The Flex Defense was also innovative in that it was a kind of zone defense against the run. Each defender was responsible for a given gap area, and was told to stay in that area before they knew where the play was going.
It has been said that, after inventing the Flex Defense, he then invented the offense to score on it, reviving the man-in-motion and the shotgun formation.
But Landry's biggest contribution in this area was the use of "pre-shifting" where the offense would shift from one formation to the other before the snap of the ball. While this tactic was not new — it was developed by Coach Amos Alonzo Stagg around the turn of the 20th Century — Landry was the first coach to use the approach on a regular basis. The idea was to break the keys the defense used to determine what the offense might do.
http://en.wikipedia.org/wiki/Tom_Landry