A style of website design which ensures that the website appears appropriately on devices with different screen sizes.
A Responsive Web Design, is the idea that your business wants to create a website that adapts to how a user is viewing it. For instance, if a visitor is viewing your website on mobile, you do not want it to be a different website than if they visited your site on a computer. By making sure your website can adapt to any resolution/screen size, your business will ensure that no visitor has a disjointed experience when visiting your website.
Also it's a philosophy of creating a website that allows all of the content to show correctly regardless of screen size or device. Your website will “respond” to the size of the screen each user has, shrinking and reorganizing on smaller screens, and expanding to fill appropriately on large ones.