Speed calculator (for calculating breakpoints/speeds) screenshot:
you see the 2 tables with "Additionaly item IAS/FCS" and "Frame" columns. Frame column says how many frames in the game it takes for the attack or spell cast it takes to be animated/done. each frame is 1/25th of a second, so if an attack takes 25 frames to finish the animation, it will take 1 second to do each attack. so if your attacks have less frames, you can do more of them in the same time. you can reduce the number of frames required for attacks by having more IAS (% Increased Attack Speed from items or skills). the "Additional item IAS" in the table in the pic tells you how much more %IAS you need to reach the next frame "breakpoint".
in the case of the screenshot, the character needs 16% more increased attack speed from items to reach 10 frames per attack (which means it would take the attack 10/25 seconds to finish = 0.4s). if the character had 37% more attack speed, it would reach 9 frames per attack, making it even faster (0.36s per attack). in this case, 9 frames is the fastest it can go with this weapon/character.
the reason why there are frames is because the game calculates and draws everything everything in steps, every second has 25 steps, so one step (or frame) is 1/25th of a second long. nothing happens in between (visually), and animations can't take for example 9.5 frames or 9.2 frames, only 9 or 10, so anything in between that is rounded to 9 or 10. that's why anything in between 16% ias and 37% ias is wasted. either get 16% to have 9 frames, or 37% to have 10. that's why they're called breakpoints, because anything between is as if nothing has changed, and then there's a step change.
it works the same with faster cast rate, faster hit recovery, etc.
speeds calculator download: http://median-xl.com/tools_files/SpeedCalc.rar