That is the current rating and they are not interchangeable
Do NOT put a higher rating (i.e. 30A) in place of a lower rating (i.e. 15A) This could cause a fire because it allows the wiring to overheat.
The reverse is OK putting a lower rated fuse in place of a higher one although your circuit will blow out the fuse at a lower current draw.
Also keep in mind fuses blowing indicate a problem, they are not usually the problem. It sounds like you did OK isolating the circuit by unplugging all the appliances but if the fuse blows when the appliances are turned-on again, either you have too many on the circuit or one of them is bad.
See if you can track down “FuseBreakers” or maybe they were called “FuseBusters” (I have them, but don’t feel like going to the basement). Basically, they screw in to replace a given rated fuse (15 for a 15, etc; also btw, 14 gauge wire gets a 15 amp fuse, 12 gauge wire gets a 20 amp fuse, 14 for 15, 12 for 20), so when they blow, one needs to locate and fix the reason (as someone already said above) and then push the button back in the center.
Ah, here’s something like what I bought, uh, over 23 years ago.
http://www.allproducts.com/prc/jgc/s101.html