Breakpoints are found in 2D games, and they refer how fast animations for attacking, spell casting, hit recovery, and many other things are displayed in frame-based games such as Diablo II.
Since Diablo 3 runs in a 3D engine, it does not have literal breakpoints; animations can display however fast or slow the game wishes. That said, there might be values that must be met in various bonuses for the improvements to become noticeable.
Breakpoints in Diablo 2
In D1 and D2, breakpoints referred to how fast animations for attacking, spell casting, hit recovery, and many other things function in frame-based games such as Diablo II. Since D2 runs at 25 frames per second, various calculations had to be increased to a certain level to show an improvement; incremental changes didn't matter.
For instance, an unmodified D2 Barbarian swung an unmodified one-handed weapon at 7 frames per second. He required 9 IAS (increased attack speed) to drop down to 6 frames, 20 IAS for 5 frames, 42 IAS for 4 frames, 86 IAS for 3 frames, and 280 IAS for 2 frames. 1 frame was not possible. So a Barbarian at 20-41 IAS was at 5 frames. Not until he reached 42 IAS did the speed of his attack become one frame quicker.
- See extensive discussion of breakpoints in the D2 section of this wiki.