What is responsive design
In short
Responsive design means a website that automatically adapts to the screen size: one view on a phone, another on a tablet, a third on a computer.
It is not a separate mobile site but one site that rearranges itself. Text, images and menu adapt to the screen.
Today responsive design is the standard. Any proper website must work well on both phone and computer.
Why responsive design matters
Most visitors open sites on a phone. If the site does not adapt, you lose much of your audience. Google also evaluates the mobile version of a site first.