Low Inductance MLCCs are used on semiconductor packages and very close to ICs on PCBs that run at high frequencies, draw a large amount of power, or have low operating voltages.  The voltage regulator that supports one or more ICs typically runs at a much lower frequency compared to the ICs it powers.  When ICs operate, the amount of power that they require varies based on what the device is doing at any moment in time.  When a large portion of the IC switches on and demands power, the slow Voltage Regulator can not provide power fast enough to keep the IC running at minimum voltage.  This is where Low Inductance MLCCs come to the rescue and provide enough power until the Voltage Regulator can react and increase the amount of power delivered to the IC.  The lower the inductance, the faster that the capacitor can react to the need for more power to the IC.