Fish do bite a lot better when it's raining. The reason is because it turns the water over. The water will be stirred up by incoming winds, making it easier to feed, especially near the surface of the water. Once the storm or rain hits, the water will be moving too much for the fish to feed. The fish will be more likely to bite just before a storm or rain because they know it may be a while before they can eat again. They'll stay out while it's raining as long as the conditions remain mild, but they'll be moving around a lot to get as much food as they can. Professional fishermen take advantage of this: This agitation may also give you an advantage in bodies of water that are normally clear: By stirring up mud, the fish won't be able to see you. This means it's much more likely to bite, and you can get away with casting closer to your boat than you would when the water is still.
When it has rained, many insect are washed into the water and the fish will be staying near the surface of water as it rains and therefore bite more. However there are other fish that hate rain and therefore go deeper under water.