If you literally dream of breathing underwater, as in you go to sleep and in your dreams you are going underwater and breathing it could mean one of several things. Since water is one area that we know seems as if it was not meant for humans (because of the fact that we don't have gills, and because of the fact that we naturally float as well as the fact that the creatures of the sea are much more well suited for sea travel and can more easily navigate waters, as well as kill us if we got into any fights.
To dream that you are able to breathe underwater would mean that you have conquered one of the things that keeps is from water the most, the fact that we cannot stay under for long periods of time without assistance. This would mean you have conquered areas that were previously off limits to you. There was some goal that you thought you would never achieve, but you were able to make it out of sheer will power. Congratulations, you should be proud of yourself for your accomplishment, it really means a lot.
It can also mean, when you dream of breathing underwater that you have conquered your fear of the water. The water is a scary place for many people, and still many more people refuse to swim in the water, especially not in open sea or in areas that seem particularly dangerous. For you to be able to go underwater and breathe means you can go anywhere in the water and probably will. You have no reason to fear drowning, so why would you ever be sacred. Try testing out in real life whether you are still afraid or not. Go take a dip in the public pool and see how you and your body react to the environment. Do you still feel scared? Use the gumption given to you by your mind to go out there and traverse the tricky waters. Maybe you don't need to go out and literally have a swim, but this spike in fearlessness shows you certainly have the will and ability to conquer other fears as well. Let's see how many you can cross off the list in the next few days now that one of the biggest ones is down.
To dream that you can breathe underwater also shows that you have obtained complete mastery over your emotions. Many times in dreams the sea or the ocean or any body of water will be representative of your emotional state. When you are on a boat, you are really showing that you have the ability to navigate through all of your complex emotional responses. However, when you are swimming in the water and don't even need a boat then this suggests that you have an even greater mastery than could have previously been seen. You are extremely in touch with yourself. Congratulations on your mastery of your own emotional climate.