First time I saw a psychiatrist I was nine or ten, so a fair bit older, but I would assume there are similarities in why/how it's done.
My experience is that a good chunk of the no-parent conversation can consist of asking some of the same questions again, maybe worded a bit differently. I guess it's to see if the child gives the same kinds of answers when there's no parent there potentially cueing certain kinds of preferred responses, inhibiting what the child feels able to say just by being there, or even actively answering for the child.
They often seem to ask questions designed to get at a better understanding of how things generally are at home from the child's perspective, and questions aimed at understanding what relationships between family members are like, how the child perceives them and so on. Not necessarily just looking for signs of abuse — obviously a kid's understanding or experience of what's going on, expectations, etc. aren't necessarily the same as how the parent assumes the kid is seeing things, and that perspective might not be able to find through with the parent there.
Then there's questions about thoughts, feelings and actions that kids might not want to reveal in front of parents, maybe things they fear would upset or worry their parents, or embarrassing things.
The specifics would be different at different ages, but this is my experience of what actually happens when the parents are asked to step out for a few minutes.