The current rating is the maximum current that an electrical circuit can handle before it experiences an overcurrent condition. In fuse boxes, there will be current ratings on each of the fuses installed that let the user know how much current it can handle. Different types of circuits may require different types of current ratings, due to building codes.
A fuse box may have a current rating on it, as well, which denotes how much current that fuse box can handle before it experiences damage or degradation.
It’s important that fuses are, in some cases, treated as troubleshooting components rather than inconveniences. Circuits that consistently blow fuses but that are provided with what appears to be the right level of current rating may actually be defective. In such cases, replacing the fuse with one with a higher current rating may actually make the entire situation more dangerous, resulting in a situation where the circuit is allowed to operate overcurrent for a prolonged period of time.