Sector 6 is one of the eight sectors of Midgar and one of the six sectors that you are able to visit. Check out the full Midgar location page for more information on the different sectors.
Sector 6 makes up two different areas of the game. It includes the maze-like area that you enter when you leave the Sector 5 Slums with Aeris and it also includes the Wall Market area. The Wall Market location has its own page - click on that link for more information.
The story takes you through Sector 6 in a transitory manner a few different times throughout the game. The first time is when Cloud and Aeris make their way to the Wall Market from Aeris’ House. Check out the bottom of the Sector 5 Slums walkthrough page for more information.
The second visit is after Cloud, Tifa and Barret confront the turks on the Sector 7 pillar. Head to the Sector 6 walkthrough page for more information on that part of the game.
You can pick up a 
Sense Materia in the playground area after the sequence involving Cloud, Barret and Tifa. Just return to the playground after the team heads south in to the maze.
The map below shows the location for Midgar on the World Map:
