A Pet Project is some idea you're working on the side. nxt supports such projects with a maxima of 20% of your work-time budget.
The topic of your project is up to you. You may contribute to open source software, improve or create additional internal tooling, solder a robot, … The rule about what is okay is simple: Everything which you are willing to explain and defend to a co-worker or to your boss is most certainly okay.
If you believe that your pet project has the potential to become a side project, please tell the management. Or build a prototype and show it.
It is possible to transfer your own pet-project time to another employee. Please ensure that such transfers are in the best interest of the company.
This is the main catch: The results of all pet projects you're engaging in becomes intellectual property of nxt by default. Contributions to open source projects are exempted from these rules where it is needed in order to make that contribution.
Talk to your superior if you would like to open source your project.