For future reference:

System level is indicative of the "development" of your star system ("is it a basic colony or a mega center of activity?"). It affects FIDSI generation and unlocks population slots on planets mainly.

You can see it here:

And it's improved from the economy screen (coin icon in screencap above) ; be sure to select the correct tab on the top left:

Then you can click the system development slot that will be highlighted (in the above it has already been chosen) and choose a luxury resource to assign to it (in the example above: Redsang).

The FIDSI bonus given by the luxury resource will be applied to the system in which you construct the system development. It is constructed like a regular system improvement, from the usual list:

As you can see it will also cost you a certain amount of the luxury resource you selected for the system development.

Hope this helps :)