It's all a matter of bandwidth. PCIe slots have more bandwidth than AGP slots. In otherwords, the slot allows information to be passed at a higher speed between the graphics card and the other parts of your computer.
But in reality, most cards don't even use the full bandwidth provided by AGP. This is why a PCIe card and an AGP card don't really perform all that differently. A PCIe version of the 6600GT (for example) and the AGP 6600GT perform about the same. The card doesn't use the full potential of the AGP slot (i.e., it is not in any way limited by the lower bandwidth of the AGP slot), and it doesn't come close to using the full bandwidth of the PCIe slot.
But PCIe is the way of the future. Since it does allow for higher bandwidth, the card makers are focusing new technology on PCIe. To be honest, I haven't done the research, but it is possible that the newest cards (X1900XT for example) may even require a bandwidth that AGP can't provide.