As @Axeman said, the connector is an Ultra Small Surface Mount Coaxial connector (quite a mouthful and still could not get how it was abbreviated as U.FL) which is a kind of expansion port which could be used for any radio communication, including GSM, WiFi, GPS.
And as @Lie Ryan said, the fourth terminal in the battery is for connecting the antennae in the battery to NFC circuitry on the motherboard. Few searches in Google confirmed this and gives raise to following information:
Those who have NFC in their phones, may lose the NFC capabilities if they try to replace with cheap and duplicate batteries which may not have the NFC antennae as said here.
I am summing up all the points to make this question as answered. I was unable to accept @Axeman's answer as complete as it did not answer the NFC part and @Lie Ryan had added as a comment only.
Kudos for them both!
Update: I happen to get hold of LG P500's service manual which confirms the RF connector with the following image tagged as SW1001.