PageRank is a measure of a site's importance and Google determines how frequently to visit the site based on the PageRank value. However PageRank is only one of the 100s of factors that Google considers while ranking sites. See Matt Cutt's comment here http://www.mattcutts.com/blog/more-info-on-pagerank/#comment-87342. So if a site genuinely does not match a search phrase, a less important site will be listed higher no matter how "important" the site is in terms of its PR.
In my opinion, PR's importance is quite minimal. There are many facters that put sites high in the SERP's. Most sites have a PR of 3-6, and I found that the other facters aside from PR is what puts these sites higher in the SERP's. It seems that PR only helps those sites with a 7+ PR.