You're going to build a browser version of something between a sketchpad and an Etch-A-Sketch.
Set up a hover effect so it changes the color of the square when your mouse passes over it, leaving a (pixelated) trail through your grid like a pen would
Add a button to the top of the screen which will clear the current grid and send the user a popup asking for how many squares per side to make the new grid. Once entered, the new grid should be generated in the same total space as before (e.g. 960px wide) and now you've got a new sketch pad.
(Optional): Instead of just changing the color of your grid from black to white (for example), have each pass through it with the mouse change to a completely random RGB value