Responsive Web Design is to allow your web site to flow according to the device being used to view your pages. With the many new devices on the market with different screen sizes, your web pages would not look very well on smaller screens if a fixed format is used. Even a fluid layout is not considered a responsive design because of its limitations of having breakpoints according to device being used to view pages.
Because most of visitors use mobile devices to search different things on the Internet. So, if you want more visitors for your website then you must have a responsive website