Indicates a very strong emotion, much more than just being upset or annoyed. After the argument, his face was like thunder.
Pro Tip 2/3
Not Literal
This is a metaphorical expression and not describing actual weather or look of a face. When the vase broke, her face was like thunder, but there was no actual storm.
Pro Tip 3/3
Social Context
Best used in casual situations, may seem out of place in formal or serious contexts. He wouldn't say why, but his face was like thunder all through dinner.