The I²t (Ampere Squared Seconds) also known as Melting Point in a fuse.
The purpose of this rating is to assure that the heat created across the fuse during a surge has insufficient time to thermally conduct away from the fuse to external circuitry. Once the measurements of current (I) and time (t) are determined, it is a simple matter to calculate melting I2t. When the melting phase reaches completion, an electrical arc occurs immediately prior to the “opening” of the fuse element.
In a fuse, you can have the same rated voltage, current, breaking capacity ratings along with being in the same response time category (slow, medium, fast) but have many different choices of the melting point. The higher the Melting Point (I2t) the longer the fuse will take to blow, and possibly more surges it may be able to handle before opening.
This is different from breaking capacity or the interrupt rating of a fuse, where these are the max amount of current at a specified voltage the fuse can handle before causing physical damage to the fuse body, exploding, or causing excessive arc upon opening. If you have ever seen a cracked glass fuse, this means the breaking capacity of the fuse has been exceeded. Sometimes this can be worse and the fuse will shatter or explode if the breaking capacity is of too low a value. This can be a danger to people and to surroundings, especially if there is flammable gas present.
Just like most electronic components, derating factors such as temperature should be applied also.
Further references are below: