This means you're nervous about something, and your stomach feels a little unsettled. Usually slightly positive though. "Knots in your stomach" would be a more negative version.

This means to feel nervous! We might say this referring to something we are nervous about but it is exciting... going on a first date or performing in a show for example!

When I was meeting John for the first time I had butterflies in my stomach. Feeling both, excited and nervous