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A Good File is a Wonderful Thing

There are a great many treatise on files available and not worth repeating here.

Files come in single or double cut. Single for finish, double for stock removal.
They come in 'Fine' and 'Bastard', where the latter means a courser tooth pattern.
They come in a great many shapes and sizes, useful for different tasks.
Larger sizes generally have relatively courser tooth patterns.
Some files have 'Safe Edges', which means the edge does not have teeth. They are useful when filing up to an edge.
There is such a thing as a 'Lathe File' with teeth designed to cut better on the outside of circular work.

Quickly shape a piece of metal. If there is not too much metal to remove, an experienced machinist can often shape a part faster with a file than it would take to set up a machine, properly secure the part, index it, and then make the cut.
Improve the finish of a part. Properly used, a file can leave a very nice finish on metal.
Improve the fit of a part. When high tolerances are required, it is common practice to leave a slight amount of material while lathing a part and then creep up on the final size with a file.
Enlarge a hole. Oddly enough, a square file is the best choice to make round holes larger.