I have encountered a number of beds and "resting places" in Aquaria, but so far they seem to have no purpose.
They are something you can interact with, the help file even mentions them as an early example of interacting, but nowhere is it mentioned that they have any use.
Other than a small push to the plot (no spoilers) in the beginning they seem to have no point at all. They could not be a save point, there are save crystals for that, and from my experience they don't seem to regenerate your health.
I have not finished the game, so if a use becomes apparent later in the game, just mention that and I'll be content.