Difficult to say exactly what since it goes back a long time. A combination of the Empire and Industrial Revolution helped a load, but of course there couldn't have been an empire without money to begin with, so really it's a case of looking back even further than that. Doing a quick bit of research it looks to be 12th/13th centuries. European economies and militaries grew due to technological innovations: windmills, mechanical clocks, distilled spirits, crop rotation, heavy plough, horse collars etc lead to economic growth; spectacles allowed academics to work longer and the use of the astrolabe resulted in better navigation.
Warfare was reformed as there was increased utilisation of specialised infantry such as crossbowmen, sappers and engineers. Armour got better as a consequence (mainly of the crossbowmen). gunpowder made it to Europe, cannons in the early 14th and hand held guns by the end of the 14th Century.
Cathedrals and Castles advanced building technology leading to large stone structures. Shipbuilding was improved, using rib and plank methods rather than the inferior Roman mortise and tenon. Sails improved, as did rudders meaning ships could sail faster.
Of course, being an island nation Britain developed [one of] the best navies in the world which came to be advantageous when it came to the wars in the Imperial days and helped cement the British Empire as the biggest empire in history (and not likely to be beaten either). This itself led to Britain becoming very wealthy and helped with the Industrial Revolution further boosting Britain's wealth and making it a world leading nation in technology.
The wealth of Britain, along with the rest of Europe (especially western Europe) and North America is primarily as a consequence of this, although the World Wars helped America somewhat.
p.s. Doing a quick bit of research brought the British East India Company back into my mind and is making me want to watch PoTC