Adaptive search is the term that refers to search engines modifying the search results (and the paid ads you see) based upon your search behavior and search profile.
In other words, two people searching on the same keyword phrase would normally (historically) see the same results organically, and more or less the same paid ads. We know that search engines such as Google rotate ads to determine which ones to serve, so two searchers may not see the same ads… but, they would see the same organic results.
However, with adaptive search, the search engines look at your past search behavior (and perhaps other factors such as clicks) as well as your profile (if you have one). Then, it customizes the search results in a manner which it feels would better suit you.
Example:
If I search for “online history degree” and several permutations of that phrase, and then refine it to remove the “history” portion, I still might see ads keyed off of the “history” portion of my phrase because the engine thinks I still may be interested in them. Engines want to make money, which means showing ads they think you’re most likely to click. So it adapts to your search pattern to show you what it feels are the most relevant results and advertisements.
This is how your advertisement might show up on a search phrase you’re not bidding on directly (exact match). So, if you have broad match, a user might see your ad even though they’ve refined their search phrase.
This is important to understand because you might start seeing clicks associated with phrases you feel are not strongly related to your business. In this case you’ll want to be careful about managing broad match in various campaigns, and you’ll also want to make sure your negative word list is kept current and you refine it by looking at poorly converting terms.
Emil Panzerino at SearchInsider for Media Post explains adaptive search quite well in his article about Bing:
http://www.mediapost.com/publications/?fa=Articles.showArticle&art_aid=159143