After acquiring a Hyperdrive you are able to visit other star systems in the galaxy.
There some 270 billion star systems in the game.
Bringing up the map view will show a 3D model of your current and adjacent sectors. Simply right click a star and then click Jump to travel to it.
If the star is not yet named, it will get your game name appended with a number incrementing from 1.
Upon arriving, selecting autopilot will show all the planets, gas giants, moons and star(s) in the local system.
When you have warped near a planet or moon, you can fly down close to it, fly along above the surface, land, even splash though under the surface of oceans and re-emerge.
Gas giants in systems usually contain large areas of Hydrogen, which can be harvested to refuel your Hyperdrive. Note that the Gas Giants in these systems are much larger than the Gas Giants in the core systems, with much more powerful gravity.
Once landed on a surface of a rocky planet or moon, you can select to have a EVA (Extra-Vehicular Activity). That is, you can don a high-tech space suit and walk around on the surface. During EVA you can take soil samples for analysis.
Premium players may claim a deed upon payment of 80 stellar credits. Upon claiming the deed you get exclusive rights to build environmental domes and associated buildings within a radius of 200 kilometres of your deed marker (square 0,0 - which cannot be built upon).