This verse is rather difficult in most of our modern English translations. It literally says, "By faith we understand the ages to have been prepared by a saying of God, in regard to the things seen not having come out of things appearing" (Young's Literal Translation).
The key to understanding this verse is the word translated "worlds" in modern Bibles. In the Greek, it is aioonas, which primarily means "ages" or long periods of time whose sum is eternity. For modern translations to understand this to be "worlds" distorts what the author was trying to explain. He is not talking about physical creation of the earth or matter, which "worlds" implies, but about God's sovereignty over the ages of mankind's civilizations. "Framed" is the Greek kateertisthai, meaning prepared, arranged, constituted, set in order—generally, to put a thing in its proper condition.
The Bible speaks of three distinct ages: the time before the Flood, the present, and the age to come (see II Peter 3:6; Galatians 1:4; Matthew 12:32; Luke 18:30; etc.). Other periods of time can be divided into distinct ages: The Babylonian, the Persian, the Greek, the Roman, the Medieval, the Renaissance, the Enlightenment, the Modern, the Postmodern, etc. The author is telling us that the word of God "prepares," "orders," or "arranges" the ages of mankind—in other words, God is sovereignly guiding the affairs of men to bring about His ultimate purpose. As is said to Daniel, "The Most High rules in the kingdom of men, gives it to whoever He will, and sets over it the lowest of men" (Daniel 4:17).
We know this by faith—that is, if we truly believe and trust God, that He is almighty, that He is bringing us to perfection, and that He has a purpose He is working out, we know that He is in control. We understand by what we read in His Word that He is working toward His ends, and what goes from His mouth (in terms of law, direction, and prophecy) will come to pass (Isaiah 55:10-11). When God speaks, things happen: It was by God speaking that the earth and everything in it was created (Genesis 1). The same is true of the migrations of nations, their rise and fall, the installation and removal of leaders, as well as the circumstances of His people in the church. God is on His throne, and He is governing His creation.
The last half of Hebrews 11:3 is our "proof": What we see going on in the world (during our age) has not been brought to pass by men but by the invisible God. Men think they are movers and shakers; they think they are in control. But God says here that events on this earth have their ultimate design in the invisible God; He rules over the kingdom of men.
There is an unseen hand manipulating events so that the person of faith can understand that history is not an endless cycle of repetition; it is going somewhere. God is drawing things to a conclusion. We are coming to the end of an age, and God is framing and manipulating events in preparation for this age to climax and end so a new and better age can begin. This verse tells us that we can see the hand of God working, not only in the big events of this world, but also in our lives if we are living by faith (II Corinthians 5:7).