Increased inductance slows down fast responses for example a chip leading to be able to draw a lot of current very quickly would stall if the inductance of its power pins prevented the current flowing when needed. For example voltage regulator chips quite often have multiple pins. The other reason as stated is to help dissipate heat. Your common surface mount regulator with eight pains will usually have for ground pins, these also act as a way of getting rid of heat into the PCB. When you are talking about very powerful packages you need the extra pains to carry the total amount of current required and to keep the inductance down so that they can draw power quickly. For example a computer processor has quite a few power pins so that they can take in the total amount of current required. The pin is not connected directly to the chip inside the IC there is a bonding wire which goes from the chip to the pin. Many people use the word chip and IC interchangeably but in actual fact they are two different things. The IC is the complete package and is made up of the chip, the bonding wires, the pins, and the plastic moulding which holds it all together. The bonding wires will also have an inductance and a current limit so as you do with wires outside you do with wires inside the IC you parallel them to increase the capacity in the same way you would use a larger PCB trace to carry more current or to reduce the inductance of the trace and make it work better at higher frequency.