I don't think we can tell from just a picture of the plugs. These are definitely two 3.5mm stereo jacks, colored headphone and mic. Maybe have a look at the manual? Or type the model number into Google? Or use a multimeter and measure the resistance.
It's for bias to the mic. Condenser mics need it to apply bias to one of the leads of the mic so it can amplify the sound before sending it to the input of the card. Some mics don't require that (self-biased) so in that case, the R pin (middle ring) goes to GND.
Ah, seems you're right. I didn't know that. But that seems to be an old way of doing it. I've only ever seen 2 contacts on a seperate microphone jack or the 4-contact combined ones in modern laptops.
Regardless, if it doesn't require the bias pin, the mic is self-biased or biased through another source (use the same wire for the signal to get bias, this is easy, you just use a cap to decouple the signal from the bias).