Flexible or responsive websites are those that fit multiple screen sizes. For the designer and developer that means they only have to work on one version of the website instead of designing one for computers and another for mobile devices.
Just a few years ago, creating a fixed website was practical. Fixed-width layouts are easier to create than flexible ones, the layouts don't break, and content doesn't overflow, but after smartphones, netbooks and tablets took off, it was almost a necessity to create websites to fit the smaller screens. In previous years mobile versions of websites were a suitable solution for many devices, but right now the variety of screen sizes makes flexible design the best answer for the present circumstances