Quantum App Store is similar to a code repository like GitHub or GitLab. It will be a digital library where the quantum developers make the code they have written for quantum computers available for others to reuse.
Currently a developer needs to know quantum programming, gates and circuits in order to write code and run on quantum computers.
But with time, quantum research starts writing more and more quantum circuits for different use cases. They will lead to creation of quantum circuit libraries for people with no expertise in quantum circuits and gates. Then all you will need to do is call the appropriate function in the programming language of your choice, from the circuit libraries; which will in turn run your code in a quantum computer to return a result.