Europe ruled much of the world at this time, having expanded her empires abroad into all the continents of the world. Significant world powers existed outside of Europe, most obviously in China, but also perhaps Brazil or Mexico. By the late 1800s and early 1900s, Japan had emulated innovations in European industry, technology, warfare and even government, and had built herself into a force to be reckoned with. But still, European dominance in colonisation and world trade placed them at the helm of much that went on in the world. Most of Africa remained uncolonised at the beginning of our game time-period, but had been filled in by the end. Tribal cultures still held independent sway over parts of the East Indies, Oceania, Australia, and even interior Asia, not to mention the American west, where frontiersmen, cattle drivers, cowboys and rival American Indian tribes earned fame that persists to this day.
Obviously, even if many lands were “uncolonised,” that’s not to say there weren’t people living in those places. But when you’re one of the most prestigious and powerful countries in the world, you’ve got ships, guns, and lots of money, so you don’t have to pay so much attention to those native populations.
If the natives are lucky, you’ll allow them to become partners in your growing international empire, instead of just treating them like common labourers. In time, these colonies may turn into full-fledged cities and provinces, and it’s up to the government whether to allow the local population voting rights or not.
There’s a lot of competition for these colonial outposts, especially if they happen to be sitting on a province where important trade goods can be found. Colonies are no small deal. Some fine tropical wood forests, for instance, may be what feeds a local furniture industry back home. The profits from either selling the furniture, or selling the wood itself, may be what propels the colonial power into Great Power status, rather than second-tier status.
Two countries may try to race to set up a colony, and if they happen to arrive at the same time, a friendly rivalry may even start, with each country trying to get the most influence over the province. Military troops will improve a country’s chances of capturing the territory before their rival, and there’s no guarantee this competition will remain peaceful. You don’t have to spark a war over it (though you may!), but a little bloodshed may be necessary to secure your “rights” over the colony.