If anyone says that the one, true God, our creator and lord, cannot be known with certainty from the things that have been made, by the natural light of human reason: let him be anathema.
This dogma is expressed in friendlier form in Chapter 2 of the council's Dogmatic Constitution on the Catholic Faith:
The same Holy mother Church holds and teaches that God, the source and end of all things, can be known with certainty from the consideration of created things, by the natural power of human reason : ever since the creation of the world, his invisible nature has been clearly perceived in the things that have been made.
This is kind of a peculiar dogma, in that it makes something about natural reason a matter of Christian faith. It's in the news, of course, because of the Intelligent Design dustups and the very public and extensive comments of Christoph Cardinal Schönborn on evolution and evolutionism. (See for example his interview with Beliefnet; link via Schonborn Sightings.)
This teaching contains several parts of interest in themselves. For one, it asserts that there is something (in fact, Someone) we can know "with certainty." If human beings are able to know things with certainty, we can toss out a bunch of modern philosophical positions. Of course, those Catholics who want to affirm Vatican I while insisting that nothing can be known with certainty will still play their games -- "I can't be certain I'm understanding this canon properly," "The Church goes beyond her competency in making dogmatic statements about epistemological matters," and so forth -- but the teaching can't be held responsible for those who refuse to accept it.
It also makes the assertion that Who can be known by the natural light of reason is none other than "the one, true God, our creator and lord." This, I think, is a stronger assertion than the old "God of the philosophers" wheeze -- or perhaps the old God of the philosophers is not the remote, featureless Cause He's sometimes taken to be. In any case, the Church asserts that from philosophy we can learn that God is one, that He is true God, that He is our creator, that He is our lord, that He is the source and the end of all things, and perhaps most importantly, that His nature is perceivable in creation.
You might run that last bit by a philosopher, but to me talk of perceiving an invisible nature goes beyond uncaused causes and unmoved movers and starts getting at the kind of God Who created this particular universe. That anything exists tells us some things about the Creator, but the things that actually have been made tell us even more.
Precisely what more we could quibble over. I suspect it's things like His love of order, His sense of beauty, His careful providence. But when you say "ever since the creation of the world, His invisible nature has been clearly perceived," it seems to me you're talking the homely philosophy of design and purpose, not the more rarefied arguments of some being having of itself its own necessity.
Again, there are those who would dismiss all such philosophizing, the plain and the fancy. Again, the dogma only tells us what is true; it doesn't say everyone will believe it.
That's a point that seems to get confused, when we say that we can know that we can know something by reason by faith. Well, people ask, which is it? Do we know that we know God with certainty by faith or by reason?
And the answer, of course, is that we can know God with certainty by reason, and that we know, "We can know God with certainty by reason," is true by faith.
It may also be that we can know, "We can know God with certainty by reason," is true by reason. Nothing prevents God from revealing what in principle we could, with the natural light of reason, work out for ourselves "after a long time, and with the admixture of many errors." But the Catholic faithful need not be beholden to human reason on this question of the capability of human reason.
So what does all this mean? I can't see how it could mean, as one person suggested, that the Council Fathers meant merely that the one, true God can be known with certainty, but not that He ever actually has been. That would be a nonsensical teaching.
It also doesn't mean the Fathers meant one can prove God exists, if by "prove" we mean demonstrate according to an argument that all must accept as sound. In fact, the teaching doesn't even speak of God's existence; it speaks of knowing Him, which is a whole different proposition. Further, it speaks in quite general terms of the capability of human reason, given God's nature and His creation; it makes no claims about the intellect or will of any particular person.
At the same time, it doesn't mean that any particular claim (much less every claim) of knowing God by reason alone is true. (This should be clear enough, given that many people argue for a cruel or indifferent god based on the world as they find it.)
But the best a person can do is reason from true premises to valid conclusions. He can't force someone to accept true premises or valid reasoning who is determined to reject them.