Many of us created two versions of our websites back in the day; a regular desktop version and a mobile version. Using some fancy code, we pushed mobile devices to a m.version of our sites while everyone else went to the regular www.version. But with the advent of responsive sites, we need a way to move all our "m." users to the new, responsive site without breaking old URLs. Google has provided some guidance on doing that.
Google's webmaster blog has provided some useful advice on managing 301 reditrects. It's not rocket science but if you're not immersed in the world of web site management it's a handy guide.
Moving to a responsive site is important for business. Google prioritises mobile-friendly sites in their search results so ensuring users can access your site from any device is important.
Back when I put my first mobile friendly site together, I needed to have two templates and needed code to redirect visitors based on browser strings to the right version of the site. But as the number of mobile devices and browsers exploded, responsive site design became the best way to accomodate everyone.
If your website isn't responsive, now is the time to sort it out.