To understand what rasterizing does, first you need to know a little about the images in the computer: Bitmapped (raster) graphics and fonts are created with tiny little dots. Object-oriented (vector) graphics and fonts are created with outlines. Output devices, like printers (except for some plotters) and monitors can only print or display images using dots, not outlines. This means that when an object-oriented graphic or font is output to a printer that prints in dots per inch (as most of them do) or to a monitor that displays in pixels (as most of them do), the outlines must be turned into dots. This process of turning the outlines of the objects into dots is called rasterizing. Everything you see on your monitor has been rasterized. Everything you print has been rasterized.
When you print object-oriented and PostScript images and fonts to an image setter, the information about building those straight lines goes through a RIP (raster image processor), a piece of hardware that stands between the computer and the image setter (printer). The software in the RIP turns the straight lines into the dots that the image setter will print, in resolutions like 1270 or 2540 dots per inch
When you output (print) to a laser printer that understands PostScript, the computer chip inside the PostScript printer rasterizes the images so they can be printed in dots, usually with a resolution of 300 to 600 dots per inch
When the image is displayed (output) on the monitor, it has actually been rasterized so that it could be created out of the pixels on the screen.
And if you have a non-Postscript printer, you should read the definition for Adobe Type Manager to better understand how that software rasterizes your fonts, both to the monitor and to the printer.