Hi Elusiver,
The diffrence is that a slow blow can withstand a transient overload in current. Meaning a high current condition that lasts for a short period. But if the high current is sustained the fuse will blow. Fast blow are the opposite end of the spectrum, where even a short overload conition will blow the fuse.
Here is a good run down on fuses.
http://en.wikipedia.org/wiki/Electric_fuse
Regards
Netwolf