The device you are asking about is called a matrix switcher. For the purpose you describe you’ll want to look into an 8x8 matrix switcher, which will give you the ability to distribute eight sources (TV/video signals) to eight displays.
Depending on what type of signal you are looking to distribute you’ll have the choice of analog with component video switching or HDMI switchers. The digital HDMI switchers will be more expensive, but they will give you the ability to handle copyright protected high-definition (HD) video.
Several companies including Key Digital Atlona, Extron, Crestron, Kramer and Aurora Multimedia all make matrix video switching products.
These types of systems can be complex when you factor in audio, control and signal transmission distances. Because of these factors video matrix switchers are best installed by professional electronics technicians due to their complexity.