Domination is having control or power over people and other things. Domination is to take over, to rule something. To have the power to do things. Control or power over another or others. The exercise of such control or power.
This situation is not just some peculiarity of Puerto Rico, but quite frequent in the history of post-World War II colonialism. After the end of that supposed "war for democracy"–in reality a fight among the competing imperialists for world domination–the "democratic" imperialists tried to dress up their continued rule of subject peoples by repackaging their colonial empires as the British "commonwealth," the "French union," the Dutch "community", and similar disguises. The Puerto Rican "commonwealth" was consciously derived from these models.