The key to a responsive website is that the content is flexible and the layout fluid across a wide range of screen sizes, resolutions and devices. Simply put, no matter what device you are using to view a website on you will have the optimal viewing experience. This includes a good method of navigation the site, a minimum amount of resizing and scrolling.
A responsive design will without a doubt improve user experience and accommodate users, whether they are on a desktop or a smartphone or tablet. In providing the best possible experience, all users will have a positive opinion of your website, increasing the chances they will return in the future.
Remember, having a responsive website means that instead of having to maintain both a desktop and a mobile version of your website, you only have to maintain a single website which is extremely cost effective in both time and money.