Colocation is a data center where equipment, space, and bandwidth are available for rental to retail customers for servers and other computing hardware.
It's looks like server rent for the most part but you're using your own server instead of renting one of their own
Mostly used by large project or companies when they didn't want to store servers at their own server rooms or need more bandwidth or/and reliability than can afford yourself locally.
You can find more information about basic definitions here.
Colocation allows you to place your server machine in someone else's rack and share their bandwidth as your own. It generally costs more than standard Web hosting, but less than a comparable amount of bandwidth into your place of business. Once you have a machine set up, you take it physically to the location of the colocation provider and install it in their rack or you rent a server machine from the colocation provider.
That company then provides an IP, bandwidth, and power to your server. Once it's up and running, you access it much like you would access a Web site on a hosting provider. The difference being that you own the hardware.
Colocation (also known as ‘co-location’ or ‘colo’) is the practice of housing privately-owned servers and networking equipment in a third party data center. Instead of keeping servers in-house, in offices or at a private data center, companies can choose to ‘co-locate’ their equipment by renting space in a colocation center. Therefore, unlike other kinds of hosting, where customers can rent space on a server owned by a hosting provider, with colocation the customer already owns the server and rents the required physical space to house it within a data center.