Before WW2 there were 8 "great powers"
Britain, France, Germany, and Italy, from western europe.
Russia, America, China, and Japan, from elsewhere.
Of these, German, France, Italy, and Japan were each totally defeated at some point during the war.
China meanwhile was not only the weakest of the 8, but was internally disorganized and divided. As well, though never totally defeated, had faced significant destruction against Japan.
This left only 3 countries to compete for the title of "Great Power" in 1945.
Oh sure, there were others who tried to make claims. Canada for example now found itself with an economy, army, navy, and so forth, that would easily put it in the top 8, but Canada was only in that position due to the weakness of their competitors.
While the USSR had been heavily damaged, they had also grown significantly. After the war they effectively closed off trade with the west, and so were self sufficient, or, at least, self sufficient enough.
The United Kingdom, however, found itself in major financial trouble. The UK was forced to borrow from the US, and the US demanded a degree of subservience from that.
While you could argue there were 3 world powers after 1945, by 1956, with the suez crisis, it was clear the UK was unable to act independently to make major changes to the world, and as such, the US was also not a great power.
And the USSR
All the other "great powers" had been defeated. Either by force of arms, ideological conflict and civil war, or economics, the only two "great powers" left were the USA and USSR.
Following the collapse of the USSR, the USA became the world's only superpower.