To mizzle means to rain in a very light way, like when the air is wet but you can't see the rain very well.
Mizzle is a light, misty kind of rain that might make things a little bit wet, but not very wet.
Examples:
It might mizzle today, so bring your umbrella.
The mizzle made everything damp.
I don't like when it mizzles because I get wet.
The mizzle is like the sky is sweating.
In the mizzle, everything looks like a dream.
The mizzle mizzled all day long.