We get asked this question quite a bit. The problem is, there are multiple reasons that are custom to each case.
A keyword can be affected by one or multiple of these top 10 reasons, in order of most likely to least likely:
1) The keyword that is ranking higher has less competition than the others
2) The keyword and page ranking are inner pages (articles, pages, posts) that are written specifically around your high ranking keyword
3) You have had previous optimization for this keyword
4) You have had previous back links built for this keyword or similar keywords (does not have to be exact spelling, word or phrase match)
5) More back links with that keywords anchor text has been accepted to more trusted websites than other keywords.
6) Your website had previous Domain Authority & Page Authority for your higher ranking keyword.
7) Your keyword's popularity got hit with a sudden influx of traffic from one or more of your articles (your site or 3rd party sites sending traffic)
8) New Google Update. Usually an animal. You rose - others fell.
9) The keyword and homepage are ranking. In this case - congratulations, your Domain & Page Authority are rising and Google sees you as an authority website.
10) The competition has not built back links or written content around that keyword since Google's latest Search Engine Ranking Position update - which MOVED YOU to where they were.
11) The "gods of Google" have chosen you to be in the Top 10.