Barrels were originally all that was available for storing wine, and also for transporting it. In the Middle Ages barrels were bigger than today and the trade worked in tonneaux, (French) or tun(nes), (English), a standard barrel and the unit of sale. The tonneau (singular) came to contain 900 litres, and ships were measured according to the number of tonneaux they could carry, usually 200 to 300. The trade in wine was so important that this measure gave rise to the universal way of measuring the capacity of ships (in tons). When road transport developed in the 18th Century, these barrels were too big for the carts and rutted roads of the time, so the barrique was developed, a quarter of the capacity of a tonneau and standardised today for the storage of wine. The barrique bordelaise (Bordeaux barrel) contains 225 litres, equivalent to 300 bottles. Bulk sales through the trade, and trade prices, are still expressed per tonneau, equivalent to 1200 bottles. The collective name for barrels, of all shapes and sizes is fût. So when you see on a French wine label Elevé en fûts or Vieilli en fûts, it means the same as en barriques, 'in barrels'.
In the Middle Ages barrels were treated simply as receptacles and many things were stored in them, for example tonneaux were used for honey and corn as well as wine. Their use today is different because it was realised that new barrels improved both the flavour and keeping qualities of wine, the better the wine the better the effect. This led to the universal use of barrel ageing for top Bordeaux wines, and those from elsewhere. More recently still, lesser vineyards have taken to ageing their wine in barrel, or at least a part of it, hence the proliferation of special selections with names like Cuvée Prestige, Réserve du Château, Cuvée Spéciale etc; and names including some member of the proprietor's family or a parcel of vines.
Barrels are made of oak (chêne) and not just any old oak. Certain oak forests in France are recognised as producing the best oak for barrel making, for example in the Limousin and Allier, and wine producers tend to have their own favourite source of oak and favourite barrel maker or makers, in accordance with the effect on their wine they are trying to achieve. This is a complex matter: the more concentrated and powerful the wine, the more new oak it will support. It is pointless putting a light Bordeaux Supérieur or one-dimensional Australian (for example!) wine into 100% new barrels. The result will be like chewing burnt planks and the fruit will be completely swamped. Such treatment is for top class wine only, notably Grand Crus, and recently for wines that are made as special selections, for example from old vines, on which the yield has been carefully reduced and the extraction pushed further than for the ordinary wine. These are wines that are seeking to imitate Grand Cru wine in concentration and power. This in fact does not always work and over-oaking is a criticism levelled at some modern wine making - the terroir is being expressed less than the work of the barrel maker! Even renewing one third of your barrels every year is a lot. This means that the other two-thirds are composed of barrels bought new the previous year and the year before that - 'one wine' and 'two wine' barrels. The barrels will continue to give something to the wine for another year or two but beyond that it is wrong to think they are doing the wine any good, they have become merely receptacles and very inconvenient ones at that, hard to clean and difficult to handle. Finally, barrels are very expensive with a new French barrel costing over £400, so be prepared to pay more for a barrel aged wine than one merely aged in a vat.