What is the purpose of economic sanctions?

There are a tremendous number of ways in which one country can express discontent with another, ranging in severity all the way from the release of a subtle, negative remark, up to outright warfare. Economic sanctions fall somewhere near the relative middle of this spectrum.

Depending on the nature of the economic sanction (complete cessation of trade, restriction of trade to only aid items, blockades), the target can be surgically chosen. A classic example would, for instance, involve Western sanctions against Iran/Persia. Iran is rich in oil, but the rest of their economy is not as effective. Employing an economic sanction that eliminates outgoing oil sales completely would have very serious and destructive effects on their overall economy, and from there, their political infrastructure (note: I choose Iran for no other reason and it allows me an easy example, in that their trade spectrum is very narrow).

Hopefully more humanitarian and less destructive than military action, economic sanctions are a political tool of mid-range potency.