This legal expression means "to speak the truth".
It's used when the lawyers question potential jurors before a trial starts; that is, conducting a voir dire. The point is to get a fair jury.
I've always found it interesting that the traditional emphasis has been on jurors telling the truth.
Yet, jurors are not the problem. It's the lawyers who need to be telling the truth.
Maybe the potential jurors should be made to do a voir dire on the lawyer.