Colocation

Colocation
Colocation means that your computer resides at an ISP and you pay a monthly fee for this with or without traffic charges. Colocations usually require you to have a 1U rackmount server so that you get 2 inches of rackspace for it, a desktop server is likely too big for the ISP to house, however those that allow one fill a market niche. The reason that ISP's prefer to put 40 1U servers into a rack is because in or near telco hotels (as they are called) the dollar per square foot or meter is fairly high. Then comes the cooling issues and the maintenance. Some Colocation places allow physical inspection and hardware maintenance once a month.

Root Server
Some ISP's offer root-servers, meaning they provide the hardware to you from the start and you manage the Operating System when you have to. In Germany a root server costs around 30 to 40 dollars a month.

VServer (Virtual Private Server, VPS)
A cheaper alternative is running a vserver on ISP hardware, (it's also being called a VPS). They use vmware or similar virtual engines to give about 8 people a server a host. A Vserver in Germany costs around 7 dollars a month. Vservers are good for the person who wants an online presence, run programs on them and has it idle half the time. Basically a stripped down colocation, with your OS of choice.