Well over 50% of users found the last app they downloaded through an app store search.
While apps' on-page SEO is important, it does not have the same meaning as it does with regular SEO. On-page SEO for the app store comprises of five major sectors.
App Title - the app title should be treated in much the same way as the H1 or Title tags in HTML. Ideally the title should include the keywords of what the app is for. For instance, a notebook would do better being called Notebook 3000 than it would being called 'Book of Things'.
Description - the description is the key area of the app for SEO. Not only should it include keywords but it should sum up the app as best it can. Like with Youtube there is a fold in the description, with the primary content being the top two sentences.
Keyword Tag - the keyword section allows for 100 characters for keywords. Use them well. Apple can combine individual words so do not use phrases if you can avoid it.
Those are the three key areas of on-page SEO from a technical point of view, however there are a couple of graphical choices that help apps sell well. These include having a great icon and including screenshots with your app. Why? The answer is simple: Much like in the same way page visits are in the SEO for a regular website, number of downloads is a ranking factor for app store SEO. The prettier the page is, the more likely it is that people will download your app.
Ratings also matter, from an off-page point of view. Unfortunately they are also a sector the app designer has little control over, only by providing a decent app.