Changing which slot a card is in changes the IRQ that gets assigned to it. I've occasionally been told that you should try and keep the most active cards on separate IRQs, but I've also been told that a decently well made card / drivers / whatever should be able to handle IRQ sharing without problems. (the key being the word "decent" I think... Promise recommends not letting their boards share IRQs, at least when you call in with problems that's the first thing they tell you to try.)
The way it works is:
Each slot has a primary, secondary, tertiary, etc IRQ assignment. There are four IRQs I believe (correct me if not) to map to. If a card uses three IRQs, then the first goes to the slot's primary IRQ and the second goes to the secondary IRQ. For one slot this might mean your card's "first" IRQ goes to number 3, and the "second" IRQ goes to number 4. Then, if you have another card plugged in the slot under it, it's "primary" IRQ might also map to IRQ 4. The motherboard manual usually puts this into a table of some sort for you to read and be throughly confused by.
99.95% of the time it doesn't matter at all which slot is which. But, if you are having wacky problems and you call tech support and they say to swap your PCI cards around a bit, that's why.