Bootstrap breakpoints set the width of your web pages when they are going to be visible in different screen width devices.
So breakpoints are the building block of the responsive design layout and you can use media query to define the breakpoints.
Media query allows you to apply CSS conditionally to your web page.
Twitter Bootstrap has the mobile-first approach so that the web page will visible properly on mobile devices with the minimum breaking point.
We use breakpoints in Bootstrap Framework when we do the PSD to Bootstrap Conversion Service.
If you want to learn more about Bootstrap 4 you can watch the video below.