Typically, a symbiotic relationship in a saltwater aquarium would consist of two animals or plants feeding off of or benefiting each other in some way. Here are a few different relationships that are prevalent.
Clown Fish and Sea Anemones
This type of symbiotic relationship is one that is most popular or heard of often. The sea anemone benefits from this relationship because the feces from the clown fish helps to fertilize it and help it grow. It also benefits because the clown fish chases away a lot of its enemies that can harm it. In return, the sea anemone can help to protect the clown fish with its stinging tentacles. These keep away the clown fish's predators. While this does happen often in the ocean, you want to make sure that it can happen in your saltwater aquarium as well. Many times the sea anemone can not thrive in that environment unless taken care of in a specific way.
Moray Eel and Cleaner Shrimp
This unique pair benefit from each other as well. The cleaner shrimp swim into the eels mouth and help to clean it out as well as cleaning out the saltwater tank. On the other hand, the moray eel protects the cleaner shrimp and allows them into its mouth.
Sponges and Algae
Sponges help to provide food and oxygen for the sponge. In return, the sponge will help to protect the algae and provide carbon dioxide for it. This relationship though takes time to develop and is often better when you add one before the other into the saltwater aquarium.
Crab and Coral
This is another popular relationship that benefits both the crab and the coral. The crab will live in or near the coral for protection and the crab protects the coral in return. One thing that you want to keep in mind though for this to happen is that the environment inside of the salt water aquarium needs to match that of the wildlife. Both of these things will have a hard time surviving and thriving off of each other if they do not live in a healthy environment. The saline needs to be at a similar level and you do not want to place either one into a brand new tank.
Basically, symbiosis is mutualistic. One animal provides something that benefits another and vice versa. However, in the case of the saltwater aquarium, you will find many different relationships between plants and animals. Each one of these is an example of a plant and animal symbiotic relationship that can occur in a saltwater tank. Overall, you will find that the plant helps to protect the fish in some way while the animal tends to help fertilize it in return. Keeping your tank similar to the conditions of a real saltwater environment will make for the most successful relationships between the plants and animals. In order for them to thrive, their environments need to match those that they are used to being in.