Both your screen and many printers use rectangular grids of pixels (the screen) or dots (the printer). Any hard edge that is not perfectly aligned with the grid mus therefore be rendered as a series of stepped horizontal or vertical segments because you can't light up only part of a pixel, or print only part of a dot (printers are a bit more complex because for traditional halftones each halftone spot is composed of many printer dots, some of which will be used, and some not, depending on the value of the spot, but it's always all of a printer dot that gets used or not). The higher the resolution of the output, the more steps can be included for any particular slope and distance, and the smoother it will appear.
Many inkjet printers and some presses, use stochastic screening or something similar to make halftones, and that method uses uniform dot sizes with varying densities of coverage (though ultimately I think it still is a grid), so rather than a larger dot for a darker area you get lots of tiny dots packed close together, and only a few tiny dots spread apart, rather than a single small dot in lighter areas. These tend to make edge jaggies less apparent.
