In Final Fantasy VII, the Shinra Tower is the headquarters of the corrupt Shinra Corporation, a Corporation that also holds all political power on the planet.
The tower is in the center of the plate that covers the slums of Midgar, and is 70 stories tall. The top 10 layers of the tower are only for the most high ranking executives of the corporation.
In the game, there is one scene early in the game where the player characters must climb to the top of the tower. They have to climb to the top of the plate, go through the first 60 levels either by walking up a hidden staircase or fighting on the elevators. They then must sneak through the top ten layers, which have a variety of different secrets to discover as well as puzzles to solve.
The gameplay aside, the tower was one of the many great ways that Squaresoft sets up the mood of the game, even though the mood is highly variable. The tower throws some of the gothic horror that the game is famous for at the player, and then on the next level has a bunch of salarymen, playing on exercise equipment and eating out of vending machines.
In many ways, it sets up a rather darkly humorous message: even in the middle of the headquarters of a organization bent on world domination, there is still ornate interior decorating.