A Datacenter to me is a place that not only offers a fast connection for their servers (DS3+), but offers guaranteed uptime with UPS backups and gas powered generators, in case the worse happens.

24/7 support on systems in case they crash or if a switch goes down would also qualify as a datacenter.

If someone is running a server farm in their basement on a DS3 connection, and has power redundancy, I guess you could call it a Datacenter