Put simply, your sovereign is your king or queen. George III was the sovereign of Great Britain and her colonies — including the American ones. At least he was until a little thing called the Revolutionary War upset everything.
Sovereign as an adjective can be used to indicate the ultimate power of a state, whether a monarchy or not, as in "Peru exercised its sovereign rights to all minerals within its borders." A sovereign is also a British gold coin with a face value of one pound sterling (with the monarch's face on it). But don't sell it for a pound, because it's worth its weight in gold — quite literally — which is a lot more than a pound is worth.