The guide number of a flash is an indication of its power. The higher the number, the more powerful the flash. Greater flash power means you can illuminate more distant objects.
A flash's guide number is calculated by multiplying the flash-to-subject distance by the aperture required for a well-exposed photograph. So if good results are produced by using f/8 for a subject 7.5 metres away, the guide number is 60 (8x7.5). To ensure good results, you need to know the sensitivity (ISO) setting used, and the distance must be measured in metres, so guide numbers are usually written as "60 (ISO 100, metres)".
You'll find a Speedlite's guide number listed at the top of its specification sheet and, once you know it, you can use the calculation above in reverse to calculate the correct exposure setting. It's just a case of dividing the guide number by the subject distance (in metres) to find the aperture needed for the exposure. For example, the Speedlite EL-100
has a guide number of 26 (ISO 100, metres), so if the subject is 6.5 metres away, you need to use an aperture of f/4 (=26/6.5) at ISO 100.
If you want to use a different ISO value, you just need to calculate the aperture for ISO 100 and then adjust accordingly. For example, if you need an aperture of f/8 at ISO 100 and you want to use ISO 200, which is increasing the ISO sensitivity by one stop, then you must reduce the aperture size by one stop to f/11 to halve the amount of light reaching the sensor and accommodate the doubling of the sensitivity or the image will be too bright.
Canon Speedlites and EOS cameras have built-in autoflash exposure systems, so there is rarely any need to become too involved in the mathematics of guide numbers, but it can be very useful to determine the maximum distance at which you can use flash with your lens using the calculation above.