Ad Rank is the order in which your ad appears on a search engine results page (SERP). There are two variables: the first is your bid (how much are you willing to pay), and the second is your quality score.
Google will recalculate your ad rank every time someone searches on the terms that trigger your ad, and so you can never simply say that you want your ad to appear at #1 all the time. Rather, it is a constantly moving target, and you need to analyze which ad position seems to drive the best ROI for your budget and goals. Typically, the most desirable ad positions are not simply a top 10 result, but whatever top positioning allows your ad to show most prominently on the page.
Usually, the premium real estate on a search engine results page is reserved for the top three ads.