Factions can be used for many usual things, teaming up with your friends in multiplayer, allowing you to use faction modules to make it able for only your faction to get into your ship, and only allowing faction members to dock on your ship. To create a faction open your inventory (I) and go to the bottom and click on Factions. Click "Create Faction" and type in the name of what you want to call it.
Personal Faction Ships/Stations:
You can also buy a Faction Module for 100,000 Credits. The Faction Module adds ownership to Ships, Space Stations, Asteroids, and Planets . The Faction Module can be destroyed, but will withstand a lot of anti-matter blasts. Therefore to destroy the Faction Module, Explosives are your best choice. Ships fitted with the Faction Module can not be destroyed within their Home-Base if the ships are landed or docked. Only one Faction module can be placed per structure.
These are the useful things that come with being part of a faction.
Ships and Stations
Big factions will probably have specific ships for different jobs, and you may get one of these to use depending on your job in the faction. Also many factions will have their own space station that you can stay in, and get resources from. E.G. A faction basing themselves on The Empire () might have a space station built to look like the death star, and on joining that faction you will be given a Tie Fighter.
Pirates are technically known as a Hostile faction in Star-Made, they not only have their pre-assigned Ships (Isanth-VI) and Turrets. Pirates also have their own Stations that can be raided once all turrets and the faction module is destroyed. Most pirate ships (75%) will drop about 16-27 random items (Quanity is random too) when they are destroyed ("Core Overheat"). When a Pirate Ship's Core overheats, players have the ability to salvage the entire ship and take the Ship Core aswell. Pirates typically Show up as RED Diamonds in your HUD, and Pirate Stations show up as ORANGE Diamonds in your HUD.
Traders are truly something to fear, but only if you are going against them. If you accidentally attack a trading post they may send ships from the trading faction to try and kill you. You can occasionally find them flying around, sometimes with a pirate following close behind.