I have been playing with Bootstrap 3's grid system and have found it to be a very clever general purpose grid system for assisting developers with the layout of their sites. It also helps lead you to developing a responsive design which adapts to the size of the screen size it is being displayed on. To help cement these concept in, I quickly created a demo site which allowed me to view bootstraps responsive design features in action.
You can find that site here.
Adjust the width of the page and see how the grids layout automatically adjusts with you. These adjustments go beyond shrinking the width of a column but allow you to specify different column sizes for specific view ports. This opens up lots of options for re-arranging your site to make it just as usable on a phone, tablet or laptop.
Bootstrap goes beyond just allowing you to apply different widths to a column within a grid though. It also provides you with the ability to show and hide columns based on the width of a page. This provides you with even more functionality to empower your sites responsive design.
How does Bootstrap do this? It's all through the use of CSS media query's. Media query's allow specific CSS to be applied when certain condition are met. In the case of the Bootstrap grid system, these conditions are based on the width of your page. Take a look at the Bootstrap 3's docs to get a better understanding of how this works and the grid system in general.
With CSS frameworks like Bootstrap, HTML5 Boilerplate and Pure, its getting harder and harder to NOT create a responsive site.