Coordinates are a set of numbers that determine the location of travel points for the ships star chart. Every star, planet, moon and asteroid within the game has a unique set of coordinates.
Coordinates have two values, X and Y. They are represented as a string of numbers in the navigation console. Under the fields for entering coordinates is a 'Find Random' button, which will generate a random set of coordinates.
The game's procedural generation engine is tied to these coordinates in a way that makes the game almost infinitely unique, but two players in different games of Starbound will find the same planet if they're at the same coordinates. This allows for community 'planet sharing', giving opportunities to share in game discoveries and unique locations. Coordinate sharing can help players locate resources, dungeons, and villages.
Each planet is generated using a very controlled engine so that when any player recalls a planet through a string of coordinates, they are going to visit the exact same location that all other players will find. From dungeons, terrain and biome type, most aspects of the planet's initial state are the same.