The treaties of Utrecht helped bring an end to the War of Spanish Succession, which had been fought from 1701 to 1713. The conflict stemmed from who would rule Spanish territories following Habsburg rulers becoming extinct in 1700. One side, backed by the previous King Charles II, supported Charles II's closest relative in the female line, Phillipe de France/ Felipe V of Spain. But the Habsburg of Austria, consisting of the closest relatives in the female line, instead thought they should have the throne. In addition, many other European nations did not wish for French royalty to extend their control over so many territories.
The war's ended up consisting of France and the Spanish loyal to Felipe V against the Holy Roman Empire, the United Kingdom, the Netherlands, Portugal, Savoy, and the Spanish supporting the archduke Charles VI.
The significance of the Utrecht treaties refers to how it divided the Spanish empire, which was the largest European kingdom of the time, and eased tensions over expanded French control in Europe. The French talked peace first with the United Kingdom, where the division of Spanish territories was essentially accepted despite the absence of either Spanish army at the meeting in London. Through these treaties, France was guaranteed all of the land it formerly took over, while recognizing British rule in Rupert's Land and Newfoundland and while also giving Acadia and half of Saint Kitts to the United Kingdom.
Felipe V, of French descent, ended up in control of Spain, though he had to cut ties to French royalty so that a union of the Spanish empire to the French empire would not come about.
In this way, opponents of French control were somewhat eased by these treaties. France, though reluctantly, was able to retain much of its land by making some concessions. And Spanish loyal to Felipe V saw their preferred ruler take the throne. But Spain itself, particularly Spanish supporters of the archduke Charles VI, saw defeat and the breaking up of the Spanish empire.
Spain ceded the Spanish Netherlands, Naples, Milan, and Sardinia to the Habsburg Monarchy in Austria. Sicily went to Savoy. Minorca and Gibraltar went to the United Kingdom. Spanish Guelders went to the Dutch, and Santíssimo Sacramento went to the Portuguese.
These treaties led to a major map change in Europe, changing the so-called 'playing field' for many key 'players' such as Spain, France, and the UK. It was a part of the decline of the Spanish Empire.
Sources: Heraldica, Wikipedia, Britannica.com