Mobile websites size their display to fit the device they are shown on. This means they will look different depending on the size of the device, whether it be an iPhone or tablet. Mobile and responsive are sometimes used interchangeably. Responsive websites respond to the device they are shown on.
Over half of all website visitors use a tablet or a smart phone and this number only continues to grow. I think that in the future only programmers, developers and graphic artists will use desktop computers. Unless your website is responsive customers will not be able to use it. In order to stay in business you will need a mobile website. You can see what your website looks like on different devices at http://mobiletest.me/
Google gives special ranking to mobile websites. You can see if your site passes the Google mobile test at https://www.google.com/webmasters/tools/mobile-friendly/