If something is said to be "food for thought" it is referring to a thought or idea that is worth carefully considering. One should not just give an answer immediately, but should rather meditate on the idea. Just as a person should slowly chew their food when eating, a person should carefully "digest" or think about the idea that is being presented. Example: The President's new proposal for economic growth is food for thought.

I am not quite sure where the phrase comes from, but it means, "this is something to think about." The food in the phrase is the subject on which the listener must think about.

it means: anything that provides mental stimulus for thinking. e.g. *here is some food for thought. *that incident gave us much food for thought.