A simple, short answer is that The Seven Years War was one of the very first Global Wars, fought largely in North America and Europe, with Britain and Prussia (aided by some smaller German states and eventually Portugal) on one side, and France, Austria, Sweden, and Spain on the other (Russia was on France's side to begin with but eventually switched sides), though, like you said, there were many other theaters, including parts of Africa, Central and South America, and even India and the Philippines.

The combination of Britain, the worlds greatest naval power at the time, and Prussia, arguably one of the strongest land powers of Europe, proved advantageous for both. Britain waged war largely at sea and in the colonies (though Britain did provide Prussia significant amounts of aid at different points in the war), while Prussia did its best to fight off the Europeans powers in Europe itself. There's a large emphasis on the North American front largely because after the war, much of France's colonies on the continent would be handed over to Britain, helping set the stage for the future histories of Canada, America, and American Natives. But a lot of the war also took place on continental Europe, where Prussia struggled for the first few years to survive an onslaught from Russia, Sweden, Austria, and France. Frederick the Great's ability to pull Prussia through the war, despite heavy early setbacks, helped show the dominant rise of Prussia as a European Power, and helped prove that Sweden (along with Spain) were no longer really to be considered "Great Powers".

It is pretty ugly. France had recently allied with Austria, Britain with Prussia. Russia sided with Austria for a time. The main theatres were central Europe, North America and India. Prussia and Austria fought each other to a standstill after a phase when Russia seemed about to conquer Prussia; Britain seized New France (much of today's Canada); and the British reduced French power in India to a few small territories. The biggest product of the global skirmish was probably British domination in Bengal, only tangentially a part of the wider struggle. The peace was largely a compromise one, but the costs deepened France's fiscal woes which helped trigger the Revolution. Britain's attempt to recover some of its own outlays from its North American colonies meanwhile contributed to the War of Independence.