Responsive means your website is designed to respond to the screen it's being viewed on, automatically resizing images and re-positioning text to give the user a better experience on their device.
Don't be fooled - user experience is critical for keeping someone moving through your website, as opposed to getting frustrated because the text is too small and going elsewhere. Also, it's free as it should be an inherent part of the way your website is designed & built.
For a great example of what a responsive vs non-responsive website looks like, check out this post: UpBound Blog - Think You Don’t Need A Mobile Site? Think Again.