Search engines simply grab the content on a page and use it for indexing. They then try to analyze what information is on the page, and use it for scoring to determine what items get written to the index and their scoring (or importance) . There are many rules for this scoring, but the search engines keep them to themselves otherwise people would try to "game" them (i.e. use blackhat SEO ), so it can be hard to predict why some content is indexed higher than others. Naturally there are some known "rules" for scoring content (e.g. text in H1 will score higher in an index, than text in small type), so it's important to ensure that you are comparing content correctly e.g. perhaps your right hand pane uses fonts/tags that highlight the content leading google to believe it's the most important etc.
For a long time the relative position of content on a page didn't matter, but google changed this in ~2012, so content "above the fold" does get a higher indexed value - if your skin has a higher right hand side that may be the effect you're seeing
http://searchenginewatch.com/article/2216227/Google-Updates-Above-the-Fold-Page-Layout-Algorithm
In general if you see odd indexing it's a good idea to take a look via tools such as http://www.browseo.net/ to ensure that your content is being seen (invalid html tags or content shown by javascript only, might mean that google/indexers ignores it) - you can also use https://support.google.com/webmasters/answer/158587?hl=en
Finally, in answer to your question, you can move content around panes and within panes, however that simply causes the html to generate in different places in the page - it does not convey any additional information to search engines