Barley Wine is traditionally a thick, viscous, treacly, dark, strong beer brewed in England in the 19th century. It does however have a reference back in ancient Greece where it was a strong alcoholic drink made with barley instead of grapes. It is thought to have originated in its current form from a rejection of all things French during times of war with them, but to have a wine strength drink on the table in upper class houses was both posh & patriotic to Britain.
The style however is forever English even though the Americans are brewing perfectly good ( & of course hoppier, more bitter ) versions. Not as much as IPA, but this style is abused a little to describe beers at 5% alcohol that are really just strong bitters. Generally the style has an alcohol level at around 7-12%, like an Old World wine.
Often a higher alcohol tolerant yeast is needed, which can give it wine-like qualities with the amount of fruity esters the cells leak out. Also a lengthy maturation in barrels can give a lactic, sour flavour to contrast with the thick sweetness in addition of course to the oak flavour.
Historically it can be used to blend with new, lower strength beer to create a new beer with complex, aged qualities, but cheaper than the original Barley Wine.
There is little distinction between a Barley Wine & an Old Ale - indeed it is fairly difficult to define either of these as several breweries produce a very strong, dark ale then call it Old Ale, Barley Wine or neither.