"Colocation" is the practice of locating your own equipment in someone else's data center. There are many reasons why a company may want to do this - perhaps they simply do not have a data center of their own to use, or they may need to spread their resources around geographically for performance, security, and/or reliability reasons.
When equipment is colocated to a data center, the company that owns the equipment is essentially renting space in the data center for that equipment - plus the necessary power and data connections, IP addresses, etc. The equipment then benefits from the redundant power and cooling, security, and other features of that data center - and the company that owns the equipment doesn't have to worry about these issues.
Colocation service plans vary in terms of the power, space and bandwidth provided to the colocated equipment. It is important to be sure that the colocation plan you choose will meet the needs of your equipment in these areas. Space can vary between a single rack unit for a single server up to multiple square feet of floor space enclosed with security caging.
It is also important to make sure that the data center where your equipment will be housed is good. Most reputable companies will have lots of information on their website about the features of their data center. You can also generally email them with any specific questions you may have. You'll want to make sure that their facility is staffed around the clock, has good security measures, and has the necessary redundant power, cooling, and network connections. You may also want to find out if they actually own their data center - they could simply be renting colocation space in someone else's data center also!