Supposedly, this is an ad which is relevant to your interest , at the difference of a contextual ad, which is relevant to the content of the page your are visiting (note that if you are visiting a page, it certainly means you have an interest for its content, and so, contextual ad becomes relevant to your interest,....)
By the way, Adsense identifies you like "Star wars", you visit a site about making cakes, you might see ads about "star wars cakes"... Ok, that's the idea... but in real life, I have the impression that "interested-based ads" are only re-targetting ads, you know, you visit a product page from Amazon, ebay, or another online store, then, for the next few days, weeks or months, you 'll keep seeing ads featuring this product, over and over ... and the worse being that, even if you already bought this product, you'll continue to see ads about it ! so where is all the smartness and AI in this ?
May be this can influence people, who were unsure to buy the product,...