All of it, it's the whole universe
it can be small because you don't actually download all the stars and systems. You simply download an algorithm containing the ability to generate all the stars and systems, and it does so using a deterministic seeded algorithm. It works like minecraft! The world is (effectively) infinite, but doesn't require that much local storage. The world is generated on the fly with "random" terrain generation that uses a seed that ensures it generates the same "random" terrain the same way every time you visit the same space. Then the only data you need to store is what you've changed!
The game is installed to C:\Users\(Your user name)\AppData\Local\Frontier_Developments
It's 5.8gb on my HDD.