A facility holding a heck of a lot of computer servers. You may use computers from one or more of Amazon's DC's or Microsoft's or Google's. Or you may pay a company who pays one of those companies. Your humble first product should not involve blueprints for a new DC of your own. For DR purposes, you may have a 'primary' DC, in one location, and a 'secondary' DC in other. See also, DR.
My book "Choose Your First Product" is available now.
It gives you 4 easy steps to find and validate a humble product idea.