What is that circle/ring around the Moon?
Short answer: It's called a Moon halo, Moon ring, winter ring or 22° halo. It's caused by moonlight being refracted (bent) through ice crystals in the atmosphere.
Moon halo from Motueka, New Zealand, 2020-08-02
Photo by Niels Oggel
Long Answer: This answer is specifically about the large well-defined ring as pictured above. This is one example of atmospheric phenomena called a halo, which includes Sun halos, light pillars, sun dogs, etc. The Moon halo is a type of "22° halo", which means it appears in a circle approximately 22 degrees around the Moon. It is a large circle, always essentially the same size.
As light passes through an ice crystal, it is refracted in a similar way to light passing through a prism. Blue wavelengths are bent more then red, which is why you might be able to see a slight rainbow effect in the circle around the Moon.
Note that there are other kinds of halo, including the 44 degrees halo (very rare) and the corona (a more diffuse circle usually caused by water droplets).
Traditionally, the Moon halo has been seen as a warning of bad weather, especially an approaching storm. However, this is unreliable.
See also: