When you apply a quantity break price to a product, it creates another variant for that product at the lower price. As long as your code is all installed correctly, it hides the lower priced version so customers can't buy it. The only way a customer can get it is if they have the specified quantity of product in their cart.
When a customer is shopping, they will see the Quantity Breaks price grid, so they know what the different price levels are. If they add the appropriate quantity to the cart, the app will switch the variant once they get to the cart and the app verifies that they have the specified quantity in their basket.
If they remove some product, no longer qualifying for the price break, the app will switch it back to the higher priced variant.