To a CPUs immediate performance, thermal paste means nothing, but give it time and heat warnings will be popping up all over your desktop. That being said, thermal paste is integral in the performance of a computer, it keeps it.. working.
The thermal paste essentially acts as liquid metal. It fills in the "gaps" the heat sink doesn't touch. If your heat sink made absolutely PERFECT contact with your CPU, you wouldn't need it...but this isn't the case. It conducts the heat, so that your heat sink can dissipate it. It's absolutely essential.