Grid based design is a layout of a webpage based on rows and columns, which help to put all elements into the correct order and alignment. As a result grid based design helps to build a responsive website.
Sinse we use not only computer monitors, but also tablets and mobile phones for Web surfing, it is important for websites to respond to the paricular screen size. Only responsive webpages will look nice accross all devices.
The idea is in a fluid layout divided on columns, where the width of each column takes a certain percentage of available space (which depends on a screen size).