I felt a pop in my foot running up stairs?

RICE. Rest, ice, compression and elevation. If it hurts to put pressure on your foot or you can see any misalignment, stay off of it and have it evaluated soon. You may have damaged a ligament. Fracture is possible. Don't ignore it! dr l.
Popping foot. There are all sorts of benign popping conditions... The foot is an amazing and complicated motion machine. In order for you to run up or down stairs....A series of muscles must fire and pull tendons which move bones and joints in a correct harmony and sequence to mobilize and support your legs and body. Benign popping is most likely the tendon movement within its sheath or against its fulcrum.
Pain? The question would be do you have any pain or swelling after you heard this. If you do you need to have it checked it asap. Also, try and place your foot thru range of motion, as well as each toe to make sure you did not rupture any tendons. If there is no pain or swelling and if you can walk normally, do not worry.