In Insights, a Breakdown allows you to segment an Event by a Property without specifying the property value. A Filter, on the other hand, allows you to specify the exact Property values that you care about.
For a gaming app, suppose you want to see how many times each level has been completed. In that case, you would select the "Level Completed" event and then Breakdown by "Current Level". The result displays how many of each level has been completed in the given time frame.
Now suppose you want to see how many of your users have completed level 1. If you select "Uniques for a Level Completed" event and then filter by "Current Level 1", the Insights report shows you how many unique users completed Level 1 in your selected time frame.