Why is Navi staring at this puddle like an idiot in the cow cave on Death Mountain?

You can try using the Sun Song or Song of Storms here - often this means that there is a special sort of fairy present that can fill your life and your magic. You can't, however, keep these fairies in jars.

Usually something in the area determines what song you should play - since there is water present, the song of storms would be your best bet.

In areas where Navi turns green you can usually get something to happen by playing the Song of Storms, the Sun Song or the Scarecrow song.

From the screenshot you included it should be the Sun Song or the Song of Storms from memory.

I played Song of Storms there, and a golden ball appeared that restored all my health and magic when it touched me. I couldn't catch it in a bottle, though.