Layered system constraint in REST API

I'm trying to get more acquainted with rest and try to understand what layered system means in REST architecture. As far as i understand it means that if API has database it should be on different machine on different server and api call it when it is needed. The same with bussines logic, if call should be passed through some logic call is transfered to some other server and executed there. This also will help to solve performance issue if it exist. Am I right? please give any additional info