When you win a war against a opponent, you can vassalize him to be a subject-Empire. This is explained on the official wiki:
A Vassal is the most controlled type of subject-Empire. They will automatically join their Overlord's wars, aggressive and defensive, and they have no autonomy when it comes to foreign policy or diplomatic relations. A vassal also runs the risk of a full diplomatic integration by their Overlord.
However, I don't find how to do a full diplomatic integration of a vassal?