"Sort Name" is used by CiviCRM for tabular search results. CiviCRM has historically just copied the Household and Organization names directly into the Sort Name field. For names such the "The Can Company" and "Tom and Jeri Cooper" this doesn't work out so well; the sort will happen on the letter T as in "The" rather than the letter C as is more appropriate.
There's good reason and popular demand that Sort Name should be a customizable field (for Individual contacts too)...but it's not so simple. There are some technical hurdles because CiviCRM must remember when to override this default behavior and preserve a saved human Sort Name preference.
Dave Greenberg has estimated $2,500 for this desired enhancement to be developed and tested. The organization I work with can afford some but not all of that. Who's interested in chipping in? Please comment below.