The "pop-up" is one of the toughest moves to master in surfing. So much focus is put on this single action because this is how you go from belly riding to actually standing and "surfing" the wave. A surfer has a lot more control on his/her feet than on his/her belly, so the faster you can get to your feet, the better, though you don't want to rush it so much that you fall over.
When it's finally time to pop-up, there are so many things happening all at once in the ocean and in your head. You have just successfully judged a wave as a good one, turned your board, paddled and caught the wave which is rushing around you and pushing you fast! You feel the rush and think "Ok, it's time to pop-up"!
In the photo above, Rachel has just caught the wave and is mid pop-up. She demonstrates good form with her head up looking at the water in front of her. Both hands are directly under her shoulders, her front foot is stepping under her chest (where her stomach was laying on the board seconds earlier) and the toes of her back foot are on the board which gives her more lift and space for the front leg to pull under her chest. I like to think of the pop-up similar to Downward Dog into Warrior Pose in yoga. The final Warrior Pose is your stance, so slide your back foot closer to your front foot, so your feet are a little more than hip distance apart. Remember to avoid getting on your knees because it off sets the balance of the board.
Soon, you won't even think about the pop-up because it becomes second nature! Good luck out there!