"Sleep number"® is a registered trademark of the mattress manufacturer Select Comfort. It has nothing to do with physiology or biology. It refers to the firmness of a mattress which can be adjusted by the owner/sleeper. Mattresses have used springs since the 19th Century, and nowadays many mattresses use air. People have invented variable mattress firmness systems in the past. A control adjusted the springs to adjust the hardness of the mattress. The sleep number system is an air bed that also has an adjustment mechanism. The mattress is divided into compartments, each of which can have a different pressure. This allows the mattress to conform to the sleeper’s body. The manufacturer says it can make sleeping more comfortable for a lot of people.
The company claims that independent tests have shown their mattresses can reduce back pain and improve overall sleep quality.
Select Comfort is based in Minneapolis and sells mattresses through many retailers. They have a big advertising campaign. They make a big deal about finding "your sleep number" and it makes a fun game for people to determine their "number", but the mattress has a dial so the number can be changed. There is little point to finding "your sleep number" before you buy the mattress. This appears to be an effective selling tactic, though.
One good thing about these sleep number beds is that they allow different firmness settings for different sides of the bed. That means that two sleeping partners can set the number to each of their preferences on their side.
Select Comfort also sells sheets and mattress pads (mattress toppers) as well as bed frames but these have nothing to do with sleep numbers.