Starting 04/21/15, mobile optimisation for websites will have a great impact on its search engine ranking. Google emphasises importance on proper display of websites on devices such as smartphones to the degree that it will now be a ranking factor in search engine optimization.
Enter the URL of your website on https://www.google.co.uk/webmasters/tools/mobile-friendly/ and click Analyze.
Additionally, you can refer to the Google Blog post for more optimisation tips.
If you are using the 1&1 MyWebsite to design your site then you are most likely already using the mobile optimised, responsive design and won't need to take any further action.
The mobile optimzed designs will automatically adapt to to any screen size and device type.
However, if you are unsure if you are using the proper design you can double check by simply clicking on the Smartphone preview button while you are in the editor. If you are using the old, non-responsive design, you will be given a notice immediately upon opening the previewer.
Please reference Google Tips for CMS-based websites for instructions and tips on all popular content management systems.
The entries in business directories are already optimised for search engines and mobile views.
Optimisation for the mobile online store has already been enabled. If you have disabled it, you can re-activate it by: Settings > General Settings > General > Mobile view and select Optimised for mobile shop.