If something happens stormily, it happens with a lot of wind, rain, and maybe thunder and lightning.
Stormily can make people think of danger, excitement, and loud noises.
Examples:
The wind blew stormily outside.
She ran home as the rain fell stormily.
The thunder crashed stormily in the sky.
The cat doesn't like it when it rains stormily.
The waves crashed stormily against the rocks.
The trees swayed stormily in the strong wind.