Which it is a product ProjeqtOr and what is its function?

Sorry I don't understand the Question.
Could you explain ?

Product is what the project works for.
A project is designed to build somthing.
It can be :
- an industrial Product (something like a prototype, ProjeQtOr is not designed to follow up production of products)
- an application (for IT projects)
- a service
...
In ProjeQtOr, it is called a Product.
So you define product, versions of product, and link version of product to project.
Then you're able to indicate on which version of product an activity stands for, or a requirement is valid for.
And you can then have version follow-up (in reports).

If you want an simple example, go to track.projector.org.
There is one only product : ProjeQtOr.
Every version of projeqtor is recorded as a version.
Every ticket is linked to a version.
This is ProjeQtOr roadmap