What does it mean that God is "sovereign"?
In addition to the passages cited above, God's sovereignty is seen in verses such as Psalm 33:11, Ephesians 1:11, and Romans 9:14-18.
When thinking about what it means that God is sovereign, I think that I tend to over-simplify and say, "God's sovereignty means that God is in control." Researching what the Bible says about God's sovereignty, Dr. Anees Zaka expands this definition significantly, writing in his book, Ten Steps In Witnessing to Muslims: "'Sovereignty' indicates ownership, authority, and control."
These concepts are, I think, tied to the roles of God in relationship to the universe, mentioned above: God is the Creator and Sustainer of all things; because He created everything, He owns everything and has absolute authority to order everything in accordance with His will, and because He sustains everything (nothing having independent existence apart from Him), He exercises control over everything.
In relation to God, Man cannot exercise sovereignty, but he is to act in submission to the divine will. Sadly, we fail to recognize our proper limits and we seek to place our desires over God's commands. Apart from God's grace, we all act as if we are owners rather than stewards, ultimate rather than subordinate authorities, and masters of our fates. This has been the natural situation of mankind from the first sin recorded in Genesis 3 until today.
Dear reader: in your own heart, who do you submit to as your sovereign? Do you seek to serve God, or do you serve yourself? Notice that even when you set standards for yourself that you constantly fall short: in big or small ways, in one area of life or another. How much more have we all fallen short of God's standards of righteousness and His glory (Rom 3:23)! But, in Christ, God has provided a way to be counted righteous and to be re-instated to live the lives we were created for, under His sovereignty. Jesus lived the life that we have not lived: a life of perfect submission to the divine will. He died in our place, to pay the penalty we deserved due to our rebellious attitudes and actions. He rose from the dead, conquering sin, death, and Hell. He now lives, offering eternal life in a right relationship with God to all who trust in Him. Trust in Christ today!