What it is
A part straight out of a quench is at its hardest and its most brittle. The martensite formed during quenching is a highly strained structure holding a great deal of internal stress. Left as it is, the part will resist wear beautifully and then crack the first time it is shocked.
Tempering reheats the part to a temperature well below the austenitising range and holds it there. Some of the trapped carbon precipitates out, the internal stresses relax, and the structure becomes tougher. Hardness drops a little; toughness rises a great deal. The temperature chosen sets where on that trade the part ends up.
Induction tempering applies the same coil-placed heat to this step. Because it is fast and local, it can be built into the same machine as the hardening operation, so a part is hardened, quenched and tempered in a single flow rather than accumulated into batches for a tempering oven.
Why induction
In line: hardening and tempering in one machine, so parts do not queue for an oven and work in progress does not pile up.
Selective: temper only the region that was hardened.
Fast: an induction temper takes a fraction of the time an oven soak does, though the cycle must still be long enough for the structure to respond.