The practice of housing privately owner servers and networking equipment in an offsite third party data center is known as colocation. Basically, some companies, wanting to avoid the hassles associated with keeping servers in-house or in office, prefer to rent space in the form of racks or cabinets and co-locate them in a colocation center.
Here they are only renting the physical space to place their own server, unlike other hosting services where the client rents space on a server owned by the service provider. Along with the physical space, the colocation service provider would also offer IP address, power, bandwidth, and cooling systems to the client so that they can successfully deploy their server.
The client can rent partial, half, or full cabinet for their server and other equipment as per their budget and requirements. This type of facility allows the clients to benefit from economies of scale that would have been impossible to achieve with an in-house server option.