Flat coil inside rechargable lithium battery
Its a coil which can be used for NFC and/or wireless charging.

For optimal performance the distance between the coil and the NFC transmitter or wireless charging pad needs te bo as small as possible so some manufacturers put these coils on the battery on some models instead of making it a sticker that is attached to the battery cover of the phone.

The battery already has some electrical contacts and it is trivial to extend that connector with more contacts and this saves placing extra contacts elsewhere in the phone.