A graphic mode or display mode primarily defines the amount of pixels, colors and frames per second that can be displayed.
For PC display modes, a mode is often described in the form Width x Height x N bpp @ fps Hz, e.g. 640 x 480 x 8bpp @ 60Hz meaning it can display 640 pixels per line, 480 pixels per column, each pixel can be one out of 256 colors (8 bits per pixel) at 60 frames per second.
Since the arrival of the DVD, home video modes are often abbreviated just by stating the number of lines that are being displayed, e.g. 720p, 1080p.
Different machines, especially early home computers and video game consoles mostly have very specific modes which can not be described in a short notation like the one given above, as they often segmented the display into Attribute Cells to save memory.