This answer will differ to some extent depending on what country you are asking about. In general, however, the core issue that separates parties on the right from those on the left is their attitude towards government involvement in the economy.
Parties of the right tend to believe in unfettered capitalism. They, like the Tories in Margaret Thatcher's time, believe in private enterprise rather than in government ownership of key industries. They, like Republicans in the US today, believe in fewer government regulations regarding such things as the environment. In other words, they want businesses to be able to do more or less as they please.
By contrast, parties of the left believe more in government intervention. They, like the Democrats in the US today, believe in things like having the government require that people buy health care. They believe in having the government regulate (as many parties in Europe want) financial markets. These are parties that feel that capitalism needs to be restrained by the government.