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 which levels active users have completed. In that case, you would select the "Active User" 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 active users are currently at Level 1. If you select "Active Users" event and then filter by "Current Level 1", the Insights report shows you how many active users are currently at Level 1 in your selected time frame.