Guide number is a flash's power rating, specified by the manufacturer at a standard ISO, used to calculate the correct aperture for a given distance to the subject.
A flash's guide number is what makes manual flash exposure a calculation instead of a run of test frames. Divide the guide number by the flash-to-subject distance and you have the f-stop that exposes the subject correctly at the rated ISO. That same relationship explains why flash falls off so fast: doubling the distance from 3 metres to 6 metres does not halve the light, it quarters it, costing two full stops.
A photographer lighting a group with one flash learns this the hard way when the front row is right and the back row, two metres further off, comes out a stop and a half dark. Guide numbers also let two units be compared honestly, since a flash quoted at GN 60 really is about one stop stronger than one at GN 40, whatever the box says about coverage or recycling time.
A speedlight is rated GN 40 in metres at ISO 100. Lighting a portrait subject 5 metres away, the maths is 40 divided by 5, which gives f/8 for a correct exposure at ISO 100. Move that subject to 2.5 metres and the required aperture becomes f/16, two stops down, because halving the distance quadruples the light.
If the shot needs f/4 for depth-of-field reasons, the flash at 5 metres is two stops too strong at full power, so either the power drops to one quarter, the flash moves back, or ISO is lowered. Zoom-head position feeds in as well: pulling the flash head from 24mm to 105mm concentrates the beam and can raise the effective guide number by a stop, while bouncing the same flash off a ceiling often costs two to three stops and makes a GN 40 unit behave like a bare GN 15 one.
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