F-number is the lens opening as a ratio of focal length to entrance pupil. Smaller number, more light, shallower depth of field, more demand on the glass in the corners. It is not a quality grade. F/1.2 is not "better" than F/2.8. It is a different trade.
In one sentence. F-number is how wide the pupil is. It buys photons and spends depth of field and edge sharpness.
What you gain when you open up
Each full stop doubles the light. F/1.4 to F/2.8 is two stops, a factor of four. That can be the difference between a usable warehouse aisle and a noisy guess. It also means a thinner slice of the world is in focus, and the edge of a wide M12 often falls apart.
What you gain when you stop down
More depth of field. Cleaner corners, up to a point. Then diffraction: the airy disk grows, and your expensive 1.4 µm pixel is smeared by physics, not by a cheap lens. Tiny pixels and tiny F-numbers do not automatically like each other, and neither do tiny pixels and very large F-numbers.
The reading-glasses test
In a dim restaurant you open your eyes wide and the menu is readable, but the candle behind it is a blur. In noon sun you squint and everything from the plate to the street is sharp, and you needed less "ISO." That is F-number, done with meat instead of glass.
How to read Camemaker
The lens library filters F-number as a range. Pick the slowest lens the scene can live with if you need depth (a dock, a shelf, a corridor). Pick a faster one if the light is poor and the subject sits in a known plane (a barcode at a fixed distance). Then check whether that fast glass still covers the format and still has MTF in the corner.