An interpolation is an interruption or an addition inserted into something spoken or written. If you’re telling someone about the wild day you had, and your best friend keeps interrupting you to add details, that’s interpolation.
Notice how interpolation looks a lot like interruption and interjection? It means something very similar. If you tell a story and then add some new parts, those are interpolations. If someone else adds new parts as you’re telling the story, that’s interpolation, too. Many ancient books have had new interpolations added every time they were printed. All interpolations add something to the original.