Today's Web is explored through a variety of screens ranging from small smartphones to giant big-screen televisions. Designing your site to work consistently across various screen sizes makes it a more pleasant experience for all visitors, regardless of the device they use to access it.
An alternative to a responsive design would be Adaptive Design, which detects the type of device being used to access the page and delivers an optimized experience specifically for smaller devices. This requires additional development to create what is essentially two different user experiences. This enables you to hide widgets or modules that wouldn't work well on a mobile device . . .