Since humans began to settle around 10,000 years ago there seems to have been large empires almost continuously, with Greeks, Romans, Ottoman, British...etc in the west and various Chinese dynasties, the Huns, Japanese and so on in the East. In addition various countries have been invaded or have attempted to have been invaded, such as with various Spanish excursions to Britain, or Germany in WWI/II. There is also the colonisation of Africa/Americas. It seems to be a mainstay.
Why did this seem to stop in the 20th century? The last empires (Ottoman, British, Japanese, USSR) ended, and although countries are invaded (e.g. Gulf war) it is not for the same purpose of expanding territory. Guesses I would make would be the rise of government and the fall of monarchies across the world, most land if not all discovered and claimed such that colonisation was impossible, and the effort needed in particular in WWII a huge strain on the powers that used to do the conquering coupled with sacrifices made by countries belonging to empires that helped earn them their independence.
There is no simple answer for this, because it wasn't something that happened overnight. Since 1946, there has been an increasingly strong international norm against redrawing borders in meaningful ways (there is still some technocratic readjustment). See here and then here for the mirror of this question, about how the international order deals with new states. Even when a country has split post-1946, it is generally along an already existing internal border. In the post-1946 understanding of the Westphalian system, borders really are sacrosanct. At least initially, this probably due to the fact World War II in Europe began as a series of demands for (somewhat reasonable) border adjustments. The norms are partially based in international law and international institutions like the UN, but these norms only have teeth when they're enforced by international actors, particularly the great powers.
While the international order has to some degree let states put up puppet regimes (Syria in Lebanon, for example), the actual act of incorporation is rare. Even attempts at it are rare. Look at, for instance, the Saddam Hussein's attempt to incorporate Kuwait, or how the world has treated Turkey's attempt to a prop up a state in North Cyprus, or the world's official non-recognition that Morocco controls Western Sahara. Sovereignty, "self-determination", and a ban on "wars of aggression" have become very strong norms that all the superpowers and all the great powers seem to have accepted.
For a somewhat longer explanation of borders in the international order and the basis of states, see here. For a systematic discussion specifically of borders, see here.