It's basically a private key we're all assigned at birth that can't be rotated. It was originally meant to be used in the state-sponsored welfare program "social security", but tons of businesses require it as a unique identifier.
I'm pretty certain you can ask them for a random number instead, as only the government is allowed (last I recall) to __require__ an SSN. I know my doctors can ask for it, but are required to accept an alternative if I don't wish to provide the SSN.