With this sort of interview they are looking for evidence that you can do research, communicate to others about your research, and that you will be able to be successful in your new program.
I think there are two ways to approach this. The first is to find an aspect of your current/previous research that will be directly applicable to your PhD project and describe that. It will directly give evidence that you have preparation and background to help you with your PhD. The alternate approach is to show that you've learned research skills that will help you face and overcome the obstacles in your new research program.
For example (from Computer Science), let's say that you're applying for a research program working on self-driving cars. In the first approach, perhaps you've worked on object recognition in images using deep neural networks. Then, you would describe the neural network architecture you used, why you used that architecture, and how you were able to classify objects in images as a result. You could then point out how this experience would be directly useful for your new research in self-driving cars.
On the other hand, suppose you've done nothing in that area. Maybe your background is in databases. Here, you might describe how you had to sanitize your data in your database to get your analysis to work - that the end techniques didn't work unless they had good incoming data. This would then show that you've learned to handle data appropriately, and when you worked on the self-driving car project, you'd have the experience in handling incoming data to be successful there.
In either case you will show that you can communicate your research, and hopefully show that you have some skills that will uniquely prepare you to take on the challenges of the new program.