EFS is a system folder in the root directory of your phone that contains very important and basic information about your device's identity like Wi-Fi MAC address, Bluetooth MAC address and the MOST IMPORTANT - IMEI address (nv_data.bin).
Now if this EFS partition accidentally gets corrupted or erased, your phone’s IMEI number will get erased and your device will become completely useless and you won't be able to make voice call further, as the carrier network will not recognize your phone. This can happen for a variety of reasons, sometimes flashing a wrong or corrupted ROM. This kind of damage is not accepted by the service center. Only solution that the service center provides is to replace the motherboard of the device and that costs a lot of $$$!
Only a BACKUP of your EFS can save your phone if something goes wrong with your EFS partition.
(Some of you have already messed up your IMEI. Check Troubleshooting forum for details.)