A datacenter is a large facility used to store web hosting equipment in optimal conditions. All aspects of the environment are precisely controlled including the temperature, humidity, fireproofing and amount of air circulated throughout the facility.
A data center is a centralized repository Computer facility designed for continuous use by several users, and well equipped with hardware, software, peripherals, power conditioning and backup, communication equipment, security systems, etc.
Known as the server farm or the computer room, the data center is where the majority of an enterprise
servers and storage are located, operated and managed
And most of the web hosting companies that say they have their own DC actually leasing rackspace in data center owned by other companies. And for more details about data center, you can consider wikipedia as well.
Datacenter is basically a facility where all the Servers are hosted in racks. Every Datacenter has it's own set of facilities which includes network, security, power supply, air conditioning systems etc.