The video card (regardless of whether it is used for 3D rendering or not) is responsible for taking data in memory and converting it to something that can be displayed. At its simplest, it's some logic to retrieve data from memory, and a character PROM which maps the character codes retrieved from memory into a signal to send to the monitor, and indeed that's exactly what the earliest video 'cards' were (think the built-in video of e.g. the Timex Sinclair). As things got more sophisticated, the video card started carrying it's own on-board RAM, developed on on-board controller (a very primitive thing that only knew how to draw lines), and offered multiple character sets, and color displays. Eventually, we got up to cards that had significant onboard acceleration for drawing lines on the screen, moving chunks of memory (bitblt), collision detection (when one element overlaps another), and even supported some of the Windows GDI commands (draw a window, etc).
Now, of course, we have 3D acceleration and all kinds of goodies.