Whatever you create on-screen, you can print (theoretically). And what you print looks pretty much like what you see on your monitor. Note that I say pretty much and not exactly. Here’s why:
Resolution differences: Your monitor resolution is much lower than your printer resolution. You may think that everything you print will look better than it does on-screen — in most cases, you’d be correct. Sometimes, however, that extra resolution makes problems that you can’t see on-screen, such as dust, dirt, scratches, and other pesky artifacts, stand out in print.
Aliasing differences: By default, Illustrator displays art and text on your monitor as anti-aliased (the edges where colors meet blend together, producing a more visually appealing image on-screen). Printed pages are not anti-aliased, and images print smoothly and cleanly.
Color differences: Your monitor displays color images by lighting up little red, green, and blue phosphorescent squares called pixels, whereas printing produces color images by applying dots of ink on paper. Creating colors by completely different physical processes causes a major difference between what you see on-screen and what you get in print.
With these points in mind, you should regularly print your artwork during the creation process to make sure that the printed result is as close as possible to what you’re designing on-screen. That way, you can modify your artwork to avoid surprises when you print the final product. After some practice, you develop an eye for what a printout will look like, even when you’re working entirely on-screen.