In this movie, a signal from deep space is discovered, and when decoded it is found to include blueprints for a machine. That machine, when constructed, creates an artificial wormhole that allows Jodie Foster's character to travel to the center of our galaxy and talk to advanced aliens--who tell her that they didn't build the wormhole tunnels; an ancient race did.
Given that Carl Sagan helped to write the screenplay, it's no surprise that it is well grounded in real ideas. The galaxy is old, far older than Earth by 8 or 9 billion years, so if there are alien civilizations out there, it's likely they are millions or even billions of years ahead of us. Look how far we've gotten in just a few millennia! Any intelligent aliens we meet could be so far advanced we might have a hard time even recognizing them as being life-forms at all.
And the traveling through wormholes? While that's all theoretical, it was based on actual physics done by Albert Einstein and his colleague Nathan Rosen. Along with 2001, Contact is considered one of the most scientifically accurate movies ever made.