paid by the government
to farmers to ensure that it remains profitable to stay a farmer, while simulataneously keeping the price of food
Farm subsidies lead to inefficiency in the economic sense, because they cause more food to be produced than the market would otherwise dictate. However, in my opinion this is not a bad thing, because the mechanisms that the market uses to correct inefficient food production are not for the weak of stomach.
Space shuttles have backup systems, and nobody complains of the inefficiency that results from that, because avoiding disaster is considered to be worth it. Similarly, farm subsidies (in principle) help shield us from certain nightmare scenarios such as the following:
Step 1: Too much food being produced. Prices fall until it is no longer profitable to be a farmer. Many farmers leave the food industry until the price of food rises high enough to make it profitable for the remaining farmers to keep farming. The land of the farmers who left is sold and/or put to other uses.
Step 2: Demand for food increases. Either the population grows, or the crops fail one year (which is actually a reduction in supply, but it has the same effect) or there is a natural disaster, or whatever.
Step 3: The price of food increases.
Step 4: The increased price of food causes more farmers to enter the market, causing the price to fall somewhat.
The problem with this scenario is that in between steps 3 and 4, people who can't afford the new, high price of food are starving. And the other problem is that it takes a very long time to move from step 3 to step 4, because once I've covered former farmland with buildings (back in step 1), it is very difficult to convert that land back to farmland.