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The "fit" of a font describes how the individual letters fit together alongside each other. A loosely fitted font has relatively large gaps between the individual letters; a closely fitted font has narrow gaps. The fit of a font makes quite a substantial difference to its general appearance.
When type was, one way or another, little metal blocks, with each letter placed on its block (save in the few cases where there was a kern) fitting was a matter of adjusting the amount of spare metal to the left and right of the actual letter (the sidebearing). Only rarely, through the use of ligatures, did the designer adjust the space between particular pairs of letters.
With digital typography, getting the side bearings "right" remains important; but it is also possible to make small adjustments for particular pairs of letters to move them a little closer or a little further apart than their sidebearings would indicate. This requires a careful eye and good judgment: it can easily be overdone.
Fit is also often adjusted by a designer if s/he is making a font for use at a particularly small size or large size: generally speaking fonts designed for smaller sizes have been more loosely fitted, and fonts designed for larger sizes have been more tightly fitted.
It was always possible to make manual adjustments to fit: tiny spaces could be inserted to make the fit looser; type could be filed down to make it tighter. But in practice the labour involved made this practical only for short texts in long sizes. Software makes it relatively easy for everyone to fiddle to their own satisfaction--but it is commonly held that since fitting is a difficult art, it is in most cases (and in all cases of doubt) best left to the designer. Opinions differ on whether "automated" fitting by software (such as InDesign's optical spacing feature) improves fit: it probably depends on the font, whether it was well-fitted to start with, and the particular task.
There is a classic discussion of the difficulties of fitting in Tracy's Letters of Credit