A responsive design is a method that forces a website to respond according to the device on which it is being viewed and delivers the appropriate output for it. Instead of designing multiple websites for devices that are sized differently, use of this approach let's the web designers design just one site but specifies within the code as to how it should appear on varied devices.
When it comes to the world of worldwide web, Size does matter. These days people are accessing internet from a variety of devices and thanks to the war between ios, android, windows and blackberry, plenty of screen sizes and resolutions are being used. An iPhone 5 with a 4" screen, an iphone 4 & 4S with a 3.5" screen, a Samsung Galaxy S4 that has a display of 5", Apple iPads with a 7.9" & 9.7" screens, Apple Macbook air with a 11.6" & 13.3" display sizes & Samsung Chromebook at 12.1", they all shows a website differently. If the design is not optimized using the responsive web design technique the user will not get the optimal viewing experience. If a website is coded using responsive web design the website will automatically resize for the device screen size it is being viewed on.
A research firm called strategy analytics, announced on October 17,2012 that the world has seen the 1 Billionth smart phone installation. It took the industry a long 16 years to achieve that landmark but the interesting part is that the next Billion of the smart phone install base is set to be achieved in less than next 3 years. Apart from smartphones there are about 250 million tablet owners that are accessing the internet from their devices.
All these people are essentially on the move while they are accessing the internet and they expect the experience to be as seamless as they would have on their desktops and laptops. A lot of important decisions are being taken by these people while on the move - They are looking for directions, booking tickets, researching what to shop and also actually buying through the devices. You surely don't want to give them a messy experience on your website where they have to zoom in and out to see various parts of it.