The term sovereign in this context?

Countries which rule themselves, as opposed to colonies or puppet states. In this specific context, JFK was exhorting people to support the UN for the sake of world peace, as agreements reached under the auspices of the UN were the best means of preserving the self-determination of small, militarily weak states without having to resort to war. He regarded the UN as a bulwark against large, powerful states (like the USSR) invading weaker countries or otherwise manipulating them (by, for example, sponsoring Communist guerrilla movements).