Power is energy per unit time. A muscle can supply the energy for a long jump, but not quickly enough to deliver it in the few milliseconds a take-off allows. Grasshoppers solve this by decoupling energy storage from energy release.
Before a jump, the large extensor tibiae muscle contracts against a flexor holding the leg folded, and a cuticular structure at the knee acts as a mechanical catch. The strain is stored in a semi-lunar process of stiff cuticle, together with resilin, an elastic protein with very high resilience that returns most of the stored energy. When the flexor relaxes, the catch releases and the stored energy discharges through the tibia in a few milliseconds, giving a power output well beyond what the muscle alone could produce.
The same catch-and-release principle appears independently in fleas, click beetles and trap-jaw ants, which is a useful check on the explanation: unrelated animals facing the same physical limit have converged on the same solution. What varies is the anatomy of the catch, and in grasshoppers its exact release mechanics are still being refined.