left: preference for some degree of state control (eg the NHS); right: preference for as much individual choice as possible (usually implying those with the most money get the best choice).
But there are lots of possible variations. Some like a state safety net to protect the old, ill and poor while still being in favour of the right of business to do what it likes. Is it socialist to have Transport for London? Shouldn't anyone have a right to buy a bus and take people where he likes at whatever fares he can get away with? There's really no one answer to this sort of question.
The actual terms come from where the different parties sat in the French parliament after the French Recolution.