The Shinra Building, also known as the Shinra Headquarters, is the huge building in the center of Midgar.
The story of the game takes you through the Shinra Building fairly early on. Check out the Shinra Building walkthrough page for more information. This is the first time your team encounters Sephiroth and begins tracking him across Gaea.
You can actually visit the Shinra Building one more time when the team revisits Midgar in Disc 2. Visiting it is optional at this point in the game, but it is the last time you can ever explore the Shinra Building and there is no way to return if you leave without picking up each of the items inside. Check out the second Midgar walkthrough page for details.
There is an item shop on the second floor that you can visit which sells the following items:
The map below shows the location of the Shinra Building (which can be found in Midgar) on the World Map: