Now, I was looking the sky when I saw the Moon showing up in a sky completely cloudy, like this:
But a little different. The clouds were doing an eye shape. What does explain that phenomenon? Looks as if moonbeams drilled through the clouds!
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Clouds are obviously not completely opaque, and what you are seeing is a break in the clouds. It is of course possible for the clouds to cover the moon, however, often the moon can shine brightly through the clouds and illuminate the clouds in some nice way.
This video might help in a visual way: https://www.youtube.com/watch?v=aLd_yhIWE48
That is called a corona. It is caused by diffraction of light by thin clouds with small but evenly sized particles. The best coronas show multiple coloured bands.
There is a similar, but unrelated, phenomenon, called a halo, which is caused by high altitude ice crystals with a regular hexagonal shape. It is much larger, 22 degrees wide.
Both these can be seen around the sun as well as the moon, and are fairly common, more common than rainbows (for example).