Not every single ad will appear on every single search. This is because the ad auction takes a variety of factors into account when determining the placement of ads on the SERP, and because not every keyword has sufficient commercial intent to justify displaying ads next to results. However, the two main factors that Google evaluates as part of the ad auction process are your maximum bid and the Quality Score of your ads.
Remember when you used to rely solely on search engines for traffic? Remember when you worked on SEO and lived and died by your placement in Google? Were you #1? Assured success. Well, okay, maybe not assured. Success only came if the keywords were relevant to your site users, but it was the only real roadmap to generating site traffic and revenue.