Breakpoints were a familiar concept from Diablo 2, where they were essential info for numerous character functions. Attack speed, casting speed, blocking speed, stun lock, etc.
D3 removed most of those variables and keyed everything to Attack Speed, and it doesn’t have any breakpoints for character attacks. There are breakpoints for pet attacks though, and the most impactful of those are the Demon Hunter’s Sentries, especially when the Marauder’s Six Piece bonus grants Sentries the ability to pewpewpew with the DH’s Hatred Spenders.
How does your DH’s attack speed translate to the attack rate of the Sentries? How many more shots will the Sentries manage if you get up to the next breakpoint? It’s complicated to calculate in your head, and Tasker and Theo just adds to the mess with the faster pet attack speed Legendary Affix. Fortunately, there are useful resources online to automate the process, and those, plus the basic function of Breakpoints are well-explained in this video by Rykhher. Demon Hunter Sentry Breakpoints Explained
The three resources mentioned in the video can be viewed here:
Here are the pics showing the two and three DH skill builds and how they are affected by each breakpoint.