Power
The guide number is an indication of how powerful the flash is, i.e. a high guide number indicates that the flash can illuminate a subject far away when shooting at a closed down f-stop. But you may not need all this power, if your subject is close to the camera (product shoots for example). So there is an element of marketing hype involved in the guide number, a bit similar to the marketing hype related to megapixels.
Back in the days when you were shooting film, the feedback cycle from shooting to seeing the result was pretty long and involved a darkroom and lots of chemicals. Back in those days, it was pretty important to calculate how far away from the camera the subject could be and still be illuminated by the flash firing. And hence the guide number was very much needed. Today, where the feedback is instantly available in the rear screen on the camera, the math involved in setting the flash power is less relevant and has been replaced by simply trial and error. Or automation in terms of TTL.
However, the guide number (often abbreviated GN) gives an indication of how powerful the flash is. Unfortunately the way to measure it differs from vendor to vendor – some shoot at ISO 100, others at ISO 200, some use reflectors, others not, and then it is not comparing apples and apples. And to confuse matters more, some give the guide number based on feet, others on meters, and this gives some significant differences obviously. But within spec sheets from the same vendor, the numbers can be compared. And as such this could be a parameter in your choice of flash, subject to your needs and preferences.
Related reading
What is stroboscopic flash photography?