When you interpolate words into a text, you alter the text by adding words in. If you’re describing your favorite novelist's work, you might interpolate a few examples of her writing into your description.
If you constantly interpolate your own snide comments into your sister's play-by-play account of an important basketball game, don't be surprised if she asks you to knock it off. In math, to interpolate means to estimate the value of something given certain data. If you’re looking at a chart that gives the level of pollutants in a lake on January 1st and February 1st, you must interpolate the level for January 15th.