_NET_WM_MOVERESIZE
The message an application sends when the user has started dragging something the application drew itself — a title bar or a resize grip — so the window manager takes over the move with its own rules.
Moving a window is the window manager's job: it holds the pointer grab, knows where the screen edges and the other windows are, and handles snapping, edge resistance and outline drawing. But a handle inside the application's own window — the resize grip in the corner of a GTK status bar, or a title bar the program painted itself — is invisible to the window manager. EWMH let the application hand over: on the button press it sends a ClientMessage of type _NET_WM_MOVERESIZE to the root window with the pointer's screen coordinates, which button is held and a direction, 0 to 7 for the eight edges and corners or 8 for a plain move. The window manager then takes the grab and carries on as if the drag had begun in its own frame.
Keyboard variants came later, starting the same modes as Alt+F7 and Alt+F8 in the mwm tradition, along with _NET_WM_MOVERESIZE_CANCEL to abort. For years the message was a curiosity for resize grips, but it became central once client-side decorations took off: every GTK 3 window with a headerbar and every Chrome window with its own title bar is moved through this call, and without it each application would have had to invent its own jerky window dragging. Wayland carried the pattern over unchanged as xdg_toplevel.move and resize, with the same handover of a press in progress.