"Left" and "right" are fairly vague terms, used to split people into convenient political groupings. They are the continental-European versions, compared with the more British/American "progressive," "liberal" and "conservative" terms. They are all a bit vague due to the different political landscapes in different countries and at different times, and the terms (particularly "liberal") can have very different meanings in different places.

Roughly speaking, and generalising horribly:

• left-leaning people/progressives feel that power structures and social hierarchies are a bad thing, and that the role of society (via government) should be to remove them,

• right-leaning people/conservatives feel that power structures and social hierarchies are a good thing, and that the role of society (via government) should be to protect them.

• centrists/liberals may feel either way about power structures and social hierarchies, but don't think the government should interfere.

Then you have groups like anarchists and libertarians, and a few others, who tend to line up somewhere with the above but might disagree on the specifics.

With both left and right you get "centre-" "hard-" and "far-" etc. depending on how extreme they take their views. Far-right people and governments tend to be in favour of use of direct force to impose power structures (to the extremes of the 1930s-40s German Government which systematically killed millions of people who didn't fit in their ideal society), while far-left people and governments can do the same to abolish power structures (e.g. the 1920s Russian Government which killed a lot of nobility and religious leaders who were part of the existing power structures).

"Left" and "right" is mostly relative, though. A "left-wing" group in one country might have similar views to a "right-wing" group in another country, depending on where the "centre" is.