The original purpose of economic sanctions is to put pressure on a government to change it's positions. However, sanctions affect the whole country and usually the ordinary people are the ones who pay the price. The argument is that it will put political pressure on the government to change by the people. As in N Korea or Iran the people suffer because of the sanctions but the wisdom is that people will eventually put enough political pressure on their government for change. While this logic is flawed, this is another discussion.
In the case of Syria, people are already revolting against the government and being punished. Sanctions are adding to people's misery and the burden is born by the people while the governing elite keeps the scarce remaining supplies.