In X Window System terminology, a display is an X server. A display can have more than one screen. The format for a display specifier string is like this:
    host:dpynumber[.screen]

For example, tftv:0.0 is display 0, screen 0, on machine tftv. tftv:0 is just plain display 0, no screen specified. If no host is specified, it's localhost.

The $DISPLAY environment variable is the default display. You can specify a specific display with most programs by giving it a -display dpyname arg. GDK (and thus also GTK+) apps take --display, not -display.

A display is done through a socket opened with Xlib call XOpenDisplay(char*), and closed with XCloseDisplay(Display*).