A fuse is rated for a specific value of current. It means it is designed to break the flow if the current exceeds the required value. If you put a fuse with a higher rating, It would allow more current in the circuit.The current in the circuit can now exceed the limit which was set earlier and can damage the appliance.
The fuses used for domestic purposes are rated as 1 A, 2 A, 3 A, 5 A, 10 A, etc.
Generally for light circuits the current rating of fuse is 5A and it is 15 A for power circuit. A high power appliance takes a high current so it needs a high rating fuse. A low power device only needs a low current so it requires a lower rating fuse. If a high rating fuse is used instead of low rating fuse, we risk the appliance overheating or being damaged.