Server side vs Client side rendering Display server

For the past few days I've been reading discussions about X.Org vs Mir vs Wayland and the way they differ from each other. I've read the following at Wikipedia: > A display server or window server is a program whose primary task is > to coordinate the input and output of its clients to and from the rest > of the operating system, the hardware, and each other. The display > server communicates with its clients over the display server protocol, > a communications protocol, which can be network-transparent or simply > network-capable. What is the server and the client on this context? Why was the rendering process made at the server before and now the approach is to let the client worry about rendering? What was the role of the client at the old days when server did the rendering, and what is the role of the server now that the client does the rendering?