Note: I do not have a very high regard for the CA, so this post may be a teeny bit biased.
The CAP is run by the EU and regulates agricultural production in European countries. It sets quotas, price floors, subsidies along with a raft of other things that make free market economists roll in their graves. It greatly distorts production and trade and is not very effective in helping out less well off farmers (most of its money goes to large, intensive farming farms) or reducing environmental degradation (as it encourages farmers to use more fertilisers and pesticides).
Not only that, since the subsidies are domestic and for exports, it impoverishes many third worl countries, particularely in Africa. There poor farmers have to compete against farmers who are payed to overproduce their crops and export the surpluses, which they just cannot effectively compete against. To make matters worse, their governments often remove any protection provided to their farmers because it is a condition of the IMF to get loans, which is good in theory, but disastrous when onely one country does it and not another (particularely when it is the third world country that cuts protection and not the developed EU).
And the CAP costs the EU countries a large portion from their hip pockets. There is a big push to get it reformed (primarily by Britain and Germany) but is finding resistance by France, Ireland and Spain.
