A 13 amp plug will usually come with a 13 amp fuse. This is the maximum amount of current an appliance can draw before the fuse blows.
When the fuse blows it's a simple job to pull the old one out with a small screwdriver and replace it. (see section on voltage/continuity tester to see how you can check fuses)
Some appliances however will come with identical plugs which have a lower rated fuse. 3 amps or 5 amps for instance. It is VERY IMPORTANT that you replace like with like. Do not use a 13 amp fuse in a appliance that stipulates a 5 amp fuse, for instance.