Your site/app responds to the screen it’s being browsed on.
More generally, it’s about responding to user need, but screen size is the most common consideration.
Your user’s viewport is their view of your site, which may be smaller than all of the content you’re trying to show.
If you have to work to adjust your site for only some of your users, you’re spending time (and money!) not providing value to the rest of your users.
The most efficient way to build things is to make them usable by everyone. This won’t always be practical, but it’s a good starting point.
It’s also the best way to build things for the long-term. How people browse the web will continue to evolve in ways we haven’t predicted.
This is often justified by the increasing number of people browsing on mobile devices.
Even if your site isn’t heavily used on mobile right now, it’s still worth considering, because doing the hardest thing first tends to lead to better results.
Restrictions breed creativity. You’ll often find simpler and more efficient ways to present your content if you start without the freedom of a large viewport.
Responsive Web Design Basics from Google’s “Web Fundamentals” guide.
Ethan Marcotte, coiner of the term “Responsive Design”, going into some detail about why it’s important.
A Government Digital Service blog post diving into how to use some of the techniques.