Mobile Responsive design, as you already know, is the ability of your website layout to adjust to the screen size of the device which is using it and the purpose of this is better user experience, e.g. working with fingers requires bigger buttons or having a small screen requires bigger text, so you can read easily.
Today, most of the people have smartphones which allows them to browse the internet from there. Having this ability makes sense to people, which have websites to make them responsive as well. Making a website responsive gives a better experience to users, as well as it will show your service in better light.
Another reason is Google Ranking. If you are a website owner, you’ve probably heard of Google Search and Ranking. Since 21st July, Google officially will rank responsive websites better.
I think this is enough of trying to convince you… if you need responsive design, give me a shout… we can do something cool together!