White light from the Sun is composed of all the colours of the rainbow. The atmosphere scatters shorter wavelengths (blue) more than longer wavelengths (red) so the sky looks blue and sunsets look red.
On a clear day the surface of the sea will reflect light from the blue sky and so will appear blue.
Hmm, at face value that sounds a reasonable explanation.
However, I've been been out on the ocean miles from land in deep water off the Hawaiian Islands and in the Indian Ocean and the water is still turquiose.
This is a question about the refraction of light. When light enters our atmosphere from the vacuum of space it refracts; changes direction. The blue end of the spectrum is refracted most and therefore we see more blue in the sky. (This is simple because there is also scatter to take account of as well).
The sea will therfore receive more blue light but also refracts light as well because it is a denser medium. Blue refracts more and the process is repeated.
If you dive to about 30m the only natural colour you see is blue. The fish must get quite a surprise when divers switch the lights on.