First and foremost, it deals with the substance of God's freedom--he does as he wants. There is nothing to restrain him, limit him, or withstand him. We could say, "nothing, except for himself," but that would be vacuous and a bit silly to point out. In a nutshell, his range of action and choice is unimpeded.
Secondly, it means that all things are under God's authority. Nothing has power over God, but God has power over all things. Nothing can compel God to do other than he wishes, yet he has the power to compel anything not him. His determination cannot be thwarted. God, alone, is in power.
Thirdly, it means all things are under God's direction. He decides how everything will be and do. There is nothing independent of God (though God is independent of all). Everything else has what capacities God determines and accomplishes what God plans. God directs the affairs of everything.
God's sovereignty is necessary, he would not be God without it. If there were something else that had the attributes of sovereignty, it would be God. However, it does not follow that some things that are attributed to God's sovereignty are necessary to sovereignty. For instance, God's sovereignty does not require that he exhaustively determine every instant of every particle's or every agent's action. It is sufficient that he governs such by law and principle put into place at creation and which operate by such capacity throughout time.
In fact, if his sovereignty did not work in this fashion, the concept of Sabbath rest would be impossible. Although he upholds (i.e. continues the existence) all things, it doesn't mean he has to be manipulating or creating things constantly, instantly, to be in control. Of course, he has the option to do what he wants, with anything he wants, anyway he wants; but generally, things proceed according to the control "program" he instituted at the initiation. They will continue that way until he says to the Creation, "Be no more."
So, things continue according to this kind of governance. Nothing is out of control, or doing other than he wills, for he sovereignly willed for things to act and be in a certain fashion. Act and be that way they will--particles do the dance they were programmed for, agents act with the capacities they were granted. God is sovereign over all, even if he did not design every instant.
This principle particularly plays out with demons and mankind. It was God's sovereign will to create these beings with a sub-sovereignty of their own. They exercise freewill, authority and direction as they do because it is God's will that they do. Agents (and even particles for that matter) do not exercise what they exercise according to the minutiae of God's determination, but by the principles of law that govern their exercise. They do as they are programmed to do, as does everything. Mankind and demon just happen to be programmed to do as they want.