The stone is an Imperial measure of weight, or possibly mass - the main one used in the United Kingdom for weighing human beings. 'Stone' is its own plural in this context, and one stone is equal to fourteen pounds. A pound, in turn, is sixteen ounces, where an ounce is the weight of a fat mouse, around 28 grams. For example, I might say that I weigh a little over twelve stone, but if I were to explain this to someone from the USA I would say I weigh 168 pounds or so (written 168lb), or I would say 72kg in pretty much the whole of the rest of the world, which has long since opted to use a system of measurement which make some kind of objective sense.
Going the other way, a stone is inexplicably one eighth of a British (or 'long') hundredweight, i.e. 112lb, which is in turn a twentieth of a ton (2240lb). Maybe it was considered bad luck for any two units to be in the same ratio as any other two units. In North America, a hundredweight actually is a hundred pounds, while a ton is still twenty hundredweights, so a British ton is 12% heavier than a ton from the other side of the Atlantic. A metric tonne is just slightly lighter than a British ton, at around 2205lb.
For a long time the stone, along with the likes of pounds and ounces, resisted any kind of standardisation. Eventually some degree of order was introduced by the avoirdupois system, which literally means 'to have some peas', but should mean 'goods of weight'. Unfortunately the stone was omitted from this convention, and the British then shoehorned it in, presumably for sentimental reasons. In the process we ruined the sense of the hundredweight, and made sure the ton was different on each side of the Atlantic. Sorry about that.
While it is quite obviously mad to use any measure which is equal to fourteen times sixteen times some other measure which is itself utterly arbitrary, there is still a case to be made for the stone as a scale for thinking about a person's weight. Its imprecision is its chief virtue - there is something to be said for people thinking of fractions of a stone as the minimum amount worth worrying about, rather than fretting over a pound here or a kilogram there, which nobody would even notice if they didn't have a set of scales to rely on. That said, imprecision is almost certainly its only virtue, so I expect Britain to keep on slowly, slowly marching towards the metrication which has been official policy for decades.