Scanners typically offer resolutions of 2,400dpi, 4,800dpi and 9,600dpi. It's important to realize that scanners simply arent capable of picking up this level of detail. The actual optical resolution of the CCDs in most modern scanners is 600 x 1,200dpi at best and all higher figures are based on interpolation.
Note that the specification of a non-uniform resolution - for example, 600 x 1200dpi - implies hardware interpolation, since the acquisition of data at 600dpi in one axis and 1200dpi in the other clearly cannot result in a 'square' of data (pixels are square). At 1200 x 1200dpi such a scanner will interpolate the 600dpi dimension up to 1200dpi. Basically, an integrated circuit chip in the scanner generates new data by taking the dots the scanner actually sees, and calculating where the dots in-between would most likely fall, using an algorithm to 'guess' the color of the new dots by averaging the color of adjacent dots.
Software interpolation can increase the resolution even more than hardware interpolation. The PC's processor is responsible for software interpolation instead of the scanner's integrated circuit chip. Also, most software interpolation algorithms are more accurate at guessing at the missing data than hardware interpolation. The problem is that best guesses can never be truly accurate. Interpolated images will often seem too smooth and slightly out of focus. This doesnt matter so much with line-art where interpolation has the effect of smoothing out jagged edges. But for continuous-tone images like photographs, it is often better to stick with a scanners actual optical resolution, where possible. If larger files are necessary, software interpolation is recommended. Where extreme interpolation is necessary, third party interpolation engines (software) that specifically perform this function yield the best results.