Responsive design means literally that design of a website (adaptive) scales with the dimensions of a screen without sacrificing text readability or usability of the user interface.

Although we tend to talk in terms of devices, it is important to look at how people use these devices. We must realize that different devices are used in different contexts. Content should therefore be precisely aligned to usage "It's about people, not devices".

After 2016, the number of web visits will be equally divided between site visitors from a desktop platform and visitors from a mobile platform. There is clearly discernible difference in behavior between visitors from these platforms. Desktop visitors may stay on average longer on the website then mobile visitors and also view more pages.
Mobile visitors are "volatile" in their search behavior. To target mobile visitors it's essential to show up on the first page of Google search results. Mobile visitors don't spend time searching for the best links on the following search result pages as desktop visitors often does.

Because future visitors for the most part will be mobile visitors it becomes important to design the website in a "mobile first" manor. Keeping in mind the 3 important aspects of development: the positions in the Google ranking, the website loading speed and user experience.

You can check out here how Google views your website based on mobile user experience and speed.
In 2015, Google has further adjusted the search algorithm allowing mobile-friendliness, speed and encryption (https) to lead a higher ranking than similar websites.