Many types of detergent, especially those high in chemicals, such as chlorine, bleach or sodium perborate, can have a negative effect on plant growth if they are present in water that the plant absorbs. Unfortunately, even soaps that are marketed as "eco-friendly" or "biodegradable" may still negatively affect plant life.
Many detergents are alkaline, which raises the pH value of water. Most plants need a very specific pH value to have optimal growth, which makes detergents a hindrance to the plant's development. That being said, some detergents contain phosphates that can actually help a plant get its nutrients to grow quickly, as long as the other chemicals to not harm the plant more.