Hopping is from the inside rear bouncing up and down in the corner when you exceed the grip limit of the outside tire and start to get slip.
Applying throttle can help plant the outside wheel harder and keep the inside rear up or it can induce a bit of powerslide, smoothing out the hopping. Hitting the brakes usually sets the inside rear down and bogs the kart off the corner.
Driving a kart through a corner relies on you putting in the correct amount of steering, throttle, and braking inputs to keep the inside off the ground smoothly. Smooth inputs = smooth kart reaction.