For the first time Shopify has reported seeing more mobile than desktop traffic on their platform. At the end of 2014 it's 50.3% to 49.7% - huge growth for a platform that didn't exist in any meaningful volumes until recently.
Conversion rates are still much lower on mobile platforms than on desktops, currently customers tend to do their research on their mobile devices and then complete the transaction on their desktop. There are a number of reasons for this - perceived security of mobile devices, difficulty of entering addresses, credit card details etc on mobile devices with small keyboards and mobile use is often 'opportunistic' - people do it when they have a few minutes but they get easily interrupted or return to their previous activity.
Research is an important part of the buying process and coherence between mobile & desktop experience is key to closing sales when a customer returns to your site on their desktop, with their credit card in hand, ready to spend on your products.
On top of measurable sales results Google is starting to make inroads to delivering better results to mobile users and now labels sites as 'mobile friendly' if they are responsive and will deliver a good user experience on your mobile device. They haven't declared that they are using these tests as search quality indicators to affect ranking but it's probably just a matter of time.
If your site isn't responsive then you're missing out on sales.
If you are stuck with a desktop only site at the moment and need to bring it up to date then get in touch. Everything we build is responsive.