Airflow is a fairly important thing in terms of keeping a computer cool. The airflow can determine the operating heat of a processor. Like aj2003 said, its the movement of air into your case, over your components, and then out of the case. In general you want more air going out of the case than going into it.
If you don't have proper airflow in your case you get ambient (non-moving) air, which just sits there trapping in heat from the components, like an oven.
If you are big in to overclocking then you're gonna want to have good airflow in order to keep your components as cool as possible.
this is even important to gamers becuase newer games need more processing power and therefore make the processor hotter, which is bad. Proper airflow can keep these temperatures down.
My comuter has three case fans. One side fan going in and two fans going out the back. This draws air flow directly over my processor heatsink fan, making it cooler. My case temps are constant mid 30s witha processor temp of mid 40s. When I had only one fan going out my case temps were constantly low 40's, which made my processor temp high 40s to mid 50s.
NEW FOR COLLEGE!:
AMD Athlon64 4000+ SanDiego
MSI K8 Neo4/SLI
eVGA GeForce 6800 GT
Corsair XMS 1 GB TwinX 3200XL (TCCD)
SoundBlaster Audigy2 ZS
2 WD 36.7 GB Raptor HDDs in RAID 0
OCZ ModStream 520W PSU
Panisonic Panflo 92mm
Thermaltake Tsunami Case