On vector graphics displays (such as the console display on the CDC 6600), the character generator would produce a series of actual strokes, which made up the character. (On the CDC 6600, each stroke could be given as 0, 1 or 2 units of distance, along the horizontal and vertical axes, from the end of the prior stroke.)
On raster displays, it was typical to store characters in the generator as an array of bits. As the beam scanned across the screen, as it got to each character (i.e. the one being displayed at that location on the screen), the appropriate sequence of bits for the current row of that character (bearing in mind that a single row of characters would encompass a number of raster scans across the screen) would be read out and used to modulate the intensity of the beam.