A 'bare-metal server' is a descriptive term for a computer server to distinguish it from modern forms of virtualization and cloud hosting. It is defined as a 'single-tenant physical server'.
Bare-metal servers have a single 'tenant'. They are not shared between customers. Each server may run any amount of work for the customer, or may have multiple simultaneous users, but they are dedicated entirely to the customer who is renting them. Unlike many servers in a data centre, they are not being shared between multiple customers.
Bare-metal servers are 'physical' servers. Each logical server offered for rental is a distinct physical piece of hardware that is a functional server on its own. They are not virtual servers running in multiple on shared hardware.
At one time, all servers were bare-metal servers. Servers were kept on-premises and often belonged to the organisation using and operating them. Operating systems developed very early on (early 1960s) to allow time-sharing. Single large computers, mainframes or minis, were commonly housed in centralised locations and their services shared through a bureau. The shift to cheap commodity PCs in the 1980s changed this as the market expanded, and most organisations, even the smallest, began to purchase or lease their own computers. Popular growth of the internet, and particularly the web, in the 1990s encouraged the practice of hosting in data centres, where many customers shared the facilities of single servers. Small web servers at this time often cost more for their connectivity than their hardware cost, encouraging this centralisation. HTTP 1.1's ability for virtual hosting also made it easy to co-host many web sites on the same server.