XDMCP is the Open Group standard, the “X Display Manager Control Protocol”. This is used to set up connections between remote systems over the network.
XDMCP is useful in multiuser situations where there are users with workstations and a more powerful server that can provide the resources to run multiple X sessions. For example, XDMCP is a good way to reuse old computers - a Pentium or even 486 computer with 16 Mb RAM is sufficient to run X itself, and using XDMCP such a computer can run a full modern KDE session from a server. For the server part, once a single KDE (or other environment) session is running, running another one requires very few extra resources.
However, allowing another method of login to your machine obviously has security implications. You should run this service only if you need to allow remote X Servers to start login sessions on your system. Users with a single UNIX® computer should not need to run this.