The nature of my site's topic is such that in my keyword research I sometimes find words that I'm not sure exactly what the visitor is searching for.
Obviously, I need to know what the searcher wants before I can build relevant content. Is there any magic way to determine exactly what (the majority of) people are searching for when they use a particular keyword?
Divining intention is one of the big jobs that search engines wrestle with. For example, on certain ambiguous keywords Google is now using a "split" results page.
It takes a lot of data-mining to get this kind of information indirectly. A user feedback form might be helpful. If you have a site search, there can be gold in monitoring those "no click" searchers or the ones who need to reformulate their query immediately.
By a no-click searcher I mean somone who doesn't click on a result and they don't refornulate the query either -- they just go elsewhere. Combine some kind of server-side click-tracking for the results page with regular log analysis and you can reveal the patterns.