Climbing shoes are important because they give you the much-needed friction on the wall and on the climbing holds. Their main benefit is the performance boost they can give you.
Climbing requires a lot of precise footwork. This precise footwork cannot be done with regular sneakers or sport shoes. Climbing shoes are designed specifically for climbing, whether it's the material the shoe is made of, or the shape of the shoe, it is all calculated and designed to give the climber the best performance possible while climbing.
While shoes are not a substitute for proper technique, body positioning, and the understanding of your body on the wall, climbing shoes give you that extra stability and variety when it comes to moving on the wall that cannot be replicated with any other shoe. This comes into play with toe hooks and catches, heel hooks and general heel usage such as pulling on the heel, standing on tiny edges, and slopers.
