When doing a standard constituent search and you get multiple possible matches, you can only open a constituent and then the search window is closed and you need to do another search if you didn't get the right constituent.
allowing the use to right clisk on the link and open in a new tab would then allow you to open multiple constituents from a single search.
This would be especially useful when looking at possible duplicate constituents as you could do the first name last name search then open all the constituents in a new tab to compare.