To keep an eye on the sky, especially to look for airplanes, birds, or other flying things.
Skywatching can be fun and interesting, especially for people who like airplanes or nature.
Examples:
We skywatch for birds in the park.
She likes to skywatch for airplanes.
Let's skywatch for shooting stars tonight.
I skywatch for UFOs just for fun.
He skywatches all day, every day, just in case something interesting flies by.
We skywatch from the roof and see many things in the sky.