To explain this concept without going into too much technical detail, it is best to think of PageRank as being comprised of two different values. One value, which we'll call "General PageRank" is nothing more than the weighting given to the links on your page. This is also the value shown in the Google Toolbar. This value is used to calculate the weighting of the links leaving your page, not your search position.
The other value we'll call "Specific PageRank." You see, if PageRank equated to search engine results rank then Yahoo, the site with the highest PR, would be listed #1 for every search result. Obviously, that wouldn't be useful, so what Google does is examine the context of your incoming links, and only those links that relate to the specific keyword being searched on will help you achieve a higher ranking for that keyword. It's very possible for a site with a lower PageRank to in fact have more on-topic incoming links than a site with a higher PageRank, in which case the site with a lower PageRank will be listed above its competitor in the search results for that term.
PageRank aside, there are also other factors that contribute Google search results -- though PageRank remains the dominant one.

