Actually, the scale was established by William Britain, when that company introduced its first hollow-cast toy soldiers at the end of the 19th century. The scale, expressed as a measurement, is 54mm. Britain measured from the ground to the top of a figure's head, excluding any additional height on a finished figure because of headgear.
The scale matched a popular common scale for toy railroads at the time.
I collect, cast and paint toy soldiers, so that's how I have that piece of trivia stuck in my head.
All of the other comments here are valid, though, too. The scale's application will vary from one manufacturer to another. And because of the natural variation of height among real people, you will probably find that you can mix figures of the same scale but of different manufacture, and have a realistic-looking result.
You may find variation in one manufacturer's figures, too, over time. I think of Monogram's 1/48th scale pilot and crew figures from their aircraft line. Their old classic pilots were smaller than their later standing figures (compare the Dauntless and Devastator pilots), and I think that the later ones might be truer to the stated scale (the old ones look closer to 1/50th, I think).
Depending on the period of history you're working with, you might deliberately mix and match figures, too. For example, I make a lot of figures from the 18th century, from the Seven Years' War and the War for Independence. The requirements for various arms of service meant that each looked for recruits with different physical characteristics. The common heavy cavalry of the day, the cuirassiers, needed relatively robust men to wear the breastplate and easily mount the larger horses they rode. So, those men tended to be larger. The Prussians recruited men who were 5' 6" or taller. The common light cavalry, the hussars, looked for men who were quicker, more agile, and mounted them on smaller horses. Again, the Prussians as an example recruited men shorter than 5' 6" for that arm.
When I look for figures of those soldiers, I know that some manufacturer's idea of 54mm gives me a more accurate figure than others. The old Stadden and Lasset castings are good for cuirassiers, but their hussars are the same height, so they don't look right. I look for those figures from makers like New Hope Design, Ulrich Puchala, Hecker & Goros.
Lately, in my branch of the hobby, some makers have stopped using the 54mm designation for 60mm, which is more accurate of their figures, and which makes things a little clearer for the modeller.
Hope that didn't bore everyone!