A Climb Speed can be used in place of Speed to traverse a vertical surface without expending the extra movement normally associated with climbing.
While you’re climbing, each foot of movement costs 1 extra foot (2 extra feet in Difficult Terrain). You ignore this extra cost if you have a Climb Speed and use it to climb.
At the DM’s option, climbing a slippery surface or one with few handholds might require a successful DC 15 Strength (Athletics) check.