Jump gates or jump points are portals to and from different systems. To use a jump gate fly up to it. Often patrolling Confed will check you for contraband as you approach. In order to use the gate you first must check to see if you have jump fuel by looking at the bar on the far right of the screen. If you don’t have any jump fuel land on a planet to refuel (automatic) and then come back. Approach the gate, fly over the blue circle in the center and while over it press the J key to initiate the jump. An animation will start, then the screen will flash and you will appear at the other end. After exiting the jump gate you might again be subjected to a contraband scan.
The circle of buoys around the gate flashing means someone, often a whole fleet, is about to come through from the other side, better clear the way.