“Where in the product development process does UX participate?”
The UX starts from an early business concept until you have a clear design of the application screens (in the case of a digital product). It also continues after that, but this is the main event.
UX Research leads to high-quality concepts
It starts by researching ways to make our target audience happy and content. Then user-centered design methodologies are used to design solutions to the problems the users have.
Read one example article I wrote about research aspects.
From an idea to a wireframe
Once you have the main idea for a solution your potential customers would need and love, UX methodologies would assist in drafting the mockups, which later will become the wireframe for the user interface.
User stories, user scenarios, and application flows
Now we can also write the use cases in which our product will be used and for which goals. These usage scenarios will define why users would like to use the product, what they want to achieve, and in what way.
This information would assist the UX designer in generating the correct interaction flows in order to make sure the user achieves their goal under their expectations. The result of this phase is a list of screen wireframes and the user action on each screen in order to achieve a specific goal or task.
Writing specification documents
Once the flows have been tested and approved, the product is ready to be developed. The UX Designer often plays a key role in writing the specification documents for developers, in order to make sure that the concepts are successfully transferred into the code as well.
Testing and validation
Lastly, the UX is also tightly connected with the quality assurance team. This is a very important link that is often neglected. The UX Designer trains the QA team on the product’s key requirements and works with them to build the test plan. This is the most effective way to ensure that the designed concepts are being tested in the correct way, rather than being forgotten under the stress of development.
For more information, I recommend reading at interaction design foundation and UX Collective (I have no affiliation with either whatsoever). Or just search online for UX, User Experience Design, or User-Centered Design.
You can also read one of my other articles on the subject. Probably this one, about the development team and creating mockups, could be a good starting point.
Good luck, and I hope this clears some doubts.