I believe the two threaded rods are holding the faucet down tight to the sink. It looks like they are allen / hex key holes on the ends of them next to the rubber tips.
I would guess you loosen those, and the faucet will come loose. It also appears you have a pullout sprayer? Sometimes you need to disconnect each of those lines and pull them out one at a time as the hole in the sink is too small to bring all the lines out at once.