Left wing/ Right wing:
Imagine the wings of a bird. The left wing tip is pure communism - total control by the govt, total equality in theory. The right wing tip is pure fascism - again, total control by the government, but private enterprise is allowed and power is purposely concentrated in the hands of a few leading in the national interest.
The wing tip analogy is show that they can be similar yet different, eg both require a stong military and nationalistic fervour to be workable.
The point of this is that left wing parties tend to favour the workers, with historical origins with unions and working classes in industrial slums of the Industrial Revolution.
Right wing parties on the other hand prefer freer enterprise and less government intervention, with less emphasis on wealth redistribution and state-provided services, and right wing governments are generally more conservative than leftist ones in social, poltical and economic terms.
However, the reality is that most of the dominant political parties in the Western democracies lies around the centre or slightly to the left or right of it. This means some, but not excessive government intervention, and some other stuff that i can't remember right now.
So, in Australia, the Labor Party is slightly to the left of centre, while the Liberal/National Parties are somewhat to the right. One Nation was more to the right than the libs, while the Greens and Democrats are more lefty than Labor.
In the US, the Democrats are the leftists, and the Republicans the right. I don't know about any other ones in the US though.
The general trend in recent years, I think, is towards more economically rational and somewhat socially conservative governments in the West, ie the rise of legitimate right wing parties in Europe and policy trends all over. However, there are a few strongly socialist countries, like the Scandinavian ones, whose strong welfare and infrastructure networks are paid for by hefty taxes. Ours is somewhat less strong, while the US is less still. (Make of that what you will) Obviously, every country is a mix of things, but that's a general picture.
I hope that all made sense and helped, sorry about the length.