I'm sure someone else will in a few minutes time provide a better answer, but I'll take a stab at it.
In my mind it is just as much about what you don't want to capture as what you do want. If you make a good desicion in what polar pattern to use, you can capture more of the original source (Singer for example), and less of the off-axis bleed (Wedge Monitors for example).
In a game of inches (Recording / Sound Reinforcement) Polar patterns have a big impact. Also, it is not un-common for mutli-pattern condensor microphones to have a different frequency response for each polar pattern.
Hope this was somewhat useful, can someone else elaborate?