Being underwater or seeing an underwater scene can have many different meanings, depending on the events and feelings going on. Some possibilities are:
The idea or feeling of "other worldly," or distant from reality
A desire to escape reality or take a break
(If the water is pressing on you or you are panicking, etc.) A feeling of overwhelm or mental/emotional smothering
The environment of your inner life at the time of the dream (for example, clear water could represent clarity of thought or feeling, and murky water could represent confusion)
The idea of going outside of your comfort zone, since water is outside a human's usual air-based environment
(If able to breath underwater or stay under a very long time) a feeling of invincibility, power, uniqueness, or specialness—or a wish to feel that way
Possible dream symbol meanings in the dream dictionary are suggested. No "standard meanings" exist because dream meaning is subjective and specific to the dreamer.