Here's how I evaluate "fit and finish".
Fit will be different depending on whether you are talking shotguns, rifles, or handguns - and then you can break it down further to revolvers and autos. But, essentially, it's the degree of precision a gun maker uses in keeping the tolerances between moving parts to a minimum. In the case of shotguns its how one indication of quality is how well the wood stock is fitted to the receiver. Gaps, unevenness, etc is an indication of cheaper work. Other types of "fit" that people will talk about is "cylinder gap" on revolvers (less being better) and slide to frame fit on autos. The theory is that the better the fit, the slicker the action.
Finish has to do with how well the receiver/frame is finished, as well as the internal parts. If you can see machine marks, the finish is a cheaper grade. See for example the Remington For example, the Remington R51 had a bad reputation for poor fit and lousy internal finish because you could see machine marks on the inside of the slide. I have a CZ 75B high polish or "glossy" blue and a Colt Ultimate Bright Stainless Gold Cup. Both look glossy/shiny at a couple feet. But, if you look at both guns with a magnifying glass you can see that the Colt has a finer polish to it and you can see swirls and lines in the CZ.