Exploration helped Britain become a world power in many ways, and I think this is such a broad question that there's no way to encompass everything within one post, however, I will try to address one aspect of British exploration that helped them become a world power (and some others, now that I'm re-reading my post) ; and that is their Navy.

It would not be unusual for a British citizen to live their entire lives wherein their country was at war with some foe that needed to be vanquished, as Britain was engaged in some form of combat with a foreign enemy from 1702 until 1799, with only a few sparse years of peace scattered throughout the century. One can only speculate of the stresses being in a constant state of war, albeit not as immediately apparent or “in the face” of Britons as something like the Blitz of London during World War Two, but ever still... a lingering shadow over their everyday lives, watching men going off to fight in exotic places perhaps never to return or hearing of the new battles and conflicts starting in odd new places half way around the world that only soon before had been terra incognito. This anxiety most likely hit fever pitch during the few times there was a very real threat of French invasion during the 18th century. Fear among the British public and Rulers was often fueled by propaganda, and British commanders even feared invasion by French ariel forces using hot air balloons, along with the possibility of the French tunneling to Britain using a Channel Tunnel. (I know this is hard to believe, but it's in the [primary!] sources)

That is not to say however, that Britain was not ready to meet these threats. To maintain their vast empire they fielded a vast army totaling 150,000 men by 1714, which had grown from just over 21,000 from the end of the 17th century. However it must be said, the standing army of Britain was never considered by her contemporaries to be the intimidating arm of the British armed forces, as Bismarck once remarked in during the 19th century when the standing army was even larger than that in the 18th century “If Lord Palmerston sends the British army to Germany, I shall have the police arrest them” – The real crown jewel of the British armed forces during this era was the Royal Navy. The Royal Navy was absolutely unmatched during this time, and it is how Britain truly became a world power through exploration.

By the end of the century it boasted a fleet of 660 ships in European waters alone. It was through this epic force that Britain controlled its colonies, trade, shipping lanes and the movement of her foes within her sphere of influence. But... that's how it worked on a Global scale, let's examine how it worked on the ground in Britain during this time;

The Royal Navy would be the backbone in which the Empire was propped up and maintained by. However, maintaining the Royal Navy, and therefore the Empire begs the question as to how they ever afforded all of this?

Being a professional sailor would now be a common career path for most young men. The Empire, which needed its vast Naval fleets to maintain itself, would not have been possible without the industry needed to properly supply and keep up to date the many facets such a force needs. For instance, in 1746, the admiralty ordered that a sum of 900,000 pounds be invested into the navy, this was on top of the 5 million pounds already invested into the British navy by that time (In 18th century pounds!). Investment into the building of ships was so great that massive timber shortages were common. With the industrial revolution building momentum, conditions in Britain were ripe to meet the challenge of having a Naval fleet that could meet challenge of exploring far flung corners of the World - Meeting this challenge were many private companies supplying and building for the Royal Navy, creating massive local economies for towns and cities such as Liverpool and Belfast – Many fortunes for average Britain’s were made during this time on the backbone of the Royal Navy.

Control of the seas and the sheer expertise of the British Navy during the 18th century would not only ensure that it was the most dominant fighting force of the time, but that Britain and her citizens could explore the globe unhindered by outside forces.

However, a lot of people just assume that British colonies touched every corner of the globe, and none of these indigenous people ever decided to see what Britain was like for themselves - That would be a wrong assumption. This time was also a time of great migration, both too and from Britain. With the Empire touching almost every corner of the globe, Britons were free to travel to far away exotic places, be it for adventure, escape, or to make their fortune. With the British Empire at one point in time or another having a grasp in 90% of countries on Earth, this gave great opportunities for Britons to travel to such places as North America, the East Indies, India and Africa.

Perhaps more rattling to native Britons during this time was by the end of the century there were an estimated 20,000 African/Black population within Britain. The exploration of the Empire had brought to British shores with it some of the first main instances of Muslim immigration to the nation. Muslim sailors, or ‘Lascars’ as they were known, that worked on British merchant shipping vessels began to make Britain home during this time . This would have had the obvious effect of making Britain of the time a much more diverse place than it was before the inception of the Empire, and would eventually go on to evolve into the incredibly diverse nation that we see in the United Kingdom today.

Sources: Ashley, Mike, The fear of invasion in British Library (http://www.bl.uk/romantics-and-victorians/articles/the-fear-of-invasion) (Mar. 2016)

Black people in Europe - International Slavery Museum, Liverpool museums” in Black people in Europe - International Slavery Museum, Liverpool museums (http://www.liverpoolmuseums.org.uk/ism/slavery/europe/black_people.aspx) (May 2016)

Butler, James Davie, “British Convicts Shipped to American Colonies” in The American Historical Review, Louis, William Roger, The Oxford history of the British Empire (Oxford, 1998)

Paxman, Jeremy, Empire: what ruling the world did to the British (London, 2012)

Wilkinson, Clive, The British Navy and the state in the eighteenth century (Woodbridge, Suffolk, UK, 2004)