The main parameters that are relevant to fuses are current capacity, arc breaking or interrupting current, speed, and energy absorption.
The current capacity is the current that the fuse will pass without blowing over any amount of time. It's the intersection of the current diagram with t=∞ and is notated in amperes.
\$ \int I^2 dt \$ is the area under the curve represented by the current squared on the Y axis, with time on the X axis. The idea is that this function looks like a hump rising up from (near) zero at a certain point, and then decreasing back to zero since the circuit is broken. Power is proportional to current squared: \$ P = I^2 R \$ , so the area under the curve is power times time, or the energy the fuse is rated to absorb. I would expect this parameter to be in kilojoules.