When sending an internet message via Starlink, a ground station will begin by using radio waves to talk to a satellite above it. Once in space, the message will be fired from satellite to satellite using lasers until it is above its destination. From there, it will be beamed down to the right ground station using radio waves again.

Source: The first detailed look at how Elon Musk’s space internet could work | New Scientist

Between distant places, this will allow messages to be sent about twice as fast as through the optical fibres on Earth that currently connect the internet, despite having to travel to space and back. This is because the speed of the signal in glass is slower than it is through space.