It's a good question and actually this is something our clients ask us fairly often. Thus, we asked our QA engineers to put together their thoughts on what is the QA process.
It turned out, that it starts earlier then many people think. Actually, it can start even earlier than the development when the client has only a general idea of what he wants. If QA team is involved at this stage, QA engineers can help to sort out all the details of the future application. Then they set to creating user stories. While doing this they also check the conformity of the client's ideas with their possible realization and help to make client's requirements clear for developers by interpreting them into user stories. They also create a documentation with test suites and test cases which is something like an encyclopedia with a collection of knowledge and rules for the project.
When it comes to development, QA engineers get to testing the app through different test types. They write bug reports to help fixing issues timely and set acceptance criteria to clearly define what results are expected to complete each user story.
So, while developers build the application, QA team makes sure that the final product and every part of the app works correctly. It happens that some of the above mentioned tasks are performed by other specialists, e.g. by project managers or developers or by clients themselves. However, performing them within the QA process helps to avoid many issues and achieve better results.
Here is a more in-depth overview of the QA process for software projects: https://anadea.info/blog/qa-engineers-working-cycle