Google traditionally indexes and evaluates the desktop version of your website. But that’s changing. The search engine has said it intends to move to indexing and evaluating the mobile version. In the meantime, it’s also running separate indexes; the mobile results are favouring (or will soon favour) sites that load quickly and use responsive design.
Now, if you already have a responsive site, and the same content appears when viewed on desktop or mobile devices, there’s no issue. But if your site has differing content, you might need to take a look at things. And if it’s not responsive (i.e. mobile devices just show a tiny version of the desktop site) then you definitely need a redesign.