If you are using a small or local web host then there is a low chance that they own their own datacenter. Your web host probably either is renting servers from a datacenter or is colocating their equipment inside someone’s datacenter. Your small or local web host would not be the only one. The practice of renting servers or colocating equipment is an industry norm.
Small or local web hosts
Most small town or local web hosts do not operate their own datacenter. Most of the time your web host has an agreement with either a larger web host or directly with a datacenter operator. This agreement maybe for renting dedicated servers or for colocating equipment.
Renting dedicated servers
The servers your web host would rent or lease are owned either by the upstream ISP or the datacenter operator. Your web host would resell the resources on these dedicated servers to local customers, like yourself. The number of servers being rented may range from a few dozen to hundreds.
Placing equipment inside a leading datacenter
Your web host may decide it would make more economical sense to “colocate” their servers and networking equipment inside someone’s datacenter rather than make their own. In this arrangement your web host would be paying for space, electricity, and bandwidth from the datacenter operator. Your web host would ship their servers and networking gear to the datacenter and let them house the equipment.