He was crucified, died, and was buried.Note that it says that he was both crucified and he died. This is not just pleonastic style, I think, but says something important about Our Lord, and about sin and death.
There is a passage in Aristotle's Posterior Analytics where he discusses different types of necessity, and one type he illustrates with an interesting example. He notes that to slaughter an animal just is to kill it, but we draw a linguistic distinction between the actual slaughtering, the slitting of the animal's throat, and the animal dying. But, Aristotle points out, once that throat is slit, the animal is as good as dead--death follows upon slaughtering as a matter of inescapable necessity, even though it is not, strictly speaking, identical to the act of slaughtering itself.
In most cases, then it would be enough to say merely "the animal was slaughtered" to know that the animal was dead, because to say that the animal was slaughtered is to say that the animal underwent an experience that literally entails death as a necessary consequence. You could say "the animal was slaughtered, and then it died," but people would look at you funny.
The words of the Creed are interesting because they include both the statement that Christ was crucified and the statement that he died. Ordinarily one might think that being crucified is a lot like being slaughtered--it seems almost to entail death as a necessary consequence, so why add the statement that he died? One reason might be to forestall possible objections to the later claim that he "rose again from the dead". If he never died as a consequence of his crucifixion, then his "rising again" would be neither "from the dead" nor, indeed, all that perplexing (though it would still be rather surprising).
But I don't think that this is the reason why the Creed is so careful in its wording. I think the reason goes deeper, and has to do with the meaning of sin and death in human experience. We believe, though the Creed does not say so, that death and decay are the physical manifestations of the sin that has pervaded creation since the Fall. They are like a sign to us that our nature has been corrupted by something for which we ourselves are responsible, and which we ourselves cannot correct on our own. When we get old, or if we get sick enough, we die, and there's no stopping that. Our souls may live on, if we are right with God, and our bodies, too, will be resurrected on the last day, if we so merit it, but we cannot control whether we physically die or not. We all do, saints and sinners alike.
Jesus of Nazareth, however, was conceived by the Holy Spirit and was entirely free from sin, both Original Sin and all subsequent sin. Thus he was immune to decay and death, as the Scriptures say. Jesus could not die of "natural" causes, because it was not in his nature to decay and die. Even crucifixion did not kill him, as slaughtering kills an animal. Each of the Gospels makes this quite clear: he did not merely "die", but in all four Gospels he is said to "give up the spirit" (Matthew: aphEken to pneuma; Mark and Luke: exepneusen; John: paredOken to pneuma). In other words, his body died as a consequence of an act of his own free will, not because decay and death had mastered it.
For this reason the Father loves me, because I lay down my life, that I may take it again. No one takes it from me, but I lay it down of my own accord. I have the power to lay it down, and I have the power to take it again; this charge I have received from my Father.Since Our Lady was also born free from Original Sin and also did not sin during her lifetime, it is tempting to see references to the "Dormition" of Our Lady in the Eastern tradition as attributing a similar sort of passage to glory to her, but this is open to some debate. "Falling asleep in the Lord" was a very common euphemism for dying, after all. But the connection betweeen sin and death seems a very important one, and it is interesting to speculate about just how seriously folks are willing to take it all. Is it just a metaphor, or do we really, genuinely make an ontological commitment to the reality of this connection?
In any case, with Jesus we are on firmer theological grounds: he only died when he himself laid down his own life, not because he was crucified. He could have hung on that cross forever if he had wanted to. Instead he chose to hang there a relatively short time (some victims lingered for many, many more hours than he did, suffering excruciating pain). He was in charge the whole time. For that we can be very grateful.