These terms are generally used to refer to the political ideology that people or political organizations hold.  The term "left" or "left-wing" is generally used to refer to more liberal ideologies while the term "right" or "right-wing" is generally used to refer to more conservative points of view.

These terms refer to a continuum of political points of view.  Most people would place communists on the far left of this spectrum.  The most common ideology to place on the far right would be fascism.  In between, there are various political positions that are more or less conservative or liberal.

These terms are used extensively in political writings.  For example, you will hear the Tory Party in England referred to as a "center-right" party, showing that they are seen as slightly more conservative than an ideology in the exact middle would be.  This is as opposed to the National Front Party in France that is seen as a far-right party.