How does a digital font stay sharp at every size?

A digital font stays sharp because most fonts store each letter as an outline made of curves, not as a picture of pixels, so it can be redrawn at any size. Outline fonts use Bézier curves and mathematical formulae to describe each glyph, which makes the character outlines scalable to any size. Most fonts used on computers today are outline fonts.

The older way was different. Bitmap fonts store each letter as a grid of pixels, and they are not scalable: a bitmap typeface requires a separate font design for each size. The limited processing power and memory of early computers forced the exclusive use of bitmap fonts. The original Mac could even produce bold by widening vertical strokes and oblique by shearing the image.

Curves have their own problem. They could not be rendered accurately at small sizes on low-resolution displays, so something more was needed. That something is hinting: mathematical instructions that adjust an outline so that it lines up with the pixel grid. At low screen resolutions, hinting is critical for producing clear, legible text.

Then comes spacing. Kerning is the adjustment of space between two specific characters. In metal type it was expensive, because the matrices had to be physically modified, so it was only used on pairs like VA or AV. With digital fonts it became much easier to kern many glyph combinations.