The Battle of Waterloo established the European status quo that would last until World War I and a period of relative peace that was unparalleled for centuries. The Congress of Vienna effectively established that the four victorious powers (UK, Prussia, Russia, Austria) would decide what Europe looked like post war. France lost territory it gained, Prussia began a German confederation.

Most importantly to world history, the UK showed the value of their economy. Despite being outnumbered 2:1 in population by France, embargoed by the entirety of Europe by the Continental system, the UK with the first truly industrial economy simply bought and paid for the militarises in Europe to do a lot of the fighting in the Napoleonic Wars. Emerging clearly as the foremost power in the world.

The UK was rewarded with small colonial outposts across the world. Each of these islands would function as naval bases giving the UK global reach, the only nation in the world to do so. This would further their dominance in the world, known as Pax Britannica (British peace).

This enforced peace by the British and their economic dominance literally shaped the world. The UK's empire grew from a few settler colonies in North America and Australia to the entirety of the Indian subcontinent, Africa from the northern to southern coasts, half of North America, Australia in its totality. British trade represented nearly two thirds of all global trade, with a lot coming from the USA which contributed to their economic growth.

The Pax Brittanica goes hand in hand with "splendid isolationism". The UK had a dual policy of not caring what Europe actually did, as long as it benefitted them, but also wanting to appear powerful if they were contradicted.

The power of the UK also ostensibly kept the Ottoman Empire afloat and turning them into a protectorate.

Now, with Prussia fast emerging as a potential second power to the UK, they started to encroach upon what the UK would consider antagonistic. As Prussia being a continental power with small coastline, they have no need to fear the Royal Navy. The Prussian chancellor claimed that they would simply arrest the British army should they intervene in Prussian matters. Eventually this would lead to the Franco-Prussian War and the creation of the German Empire.

A lot of these factors would directly lead to the First World War (and by extension the Second and Cold War) so they immediately spring to mind, but there are many more factors.