Responsive design is a way of building a website so that one set of pages rearranges itself to fit whatever screen is looking at it: a phone, a tablet, a laptop or a wide monitor. Columns stack, menus collapse, images shrink and text stays readable, without a separate mobile site or a mobile app.
It has been the standard way to build for over a decade, and every modern theme on WordPress or Shopify is responsive by default. So when a proposal lists mobile-friendly or responsive as a feature, it is listing the floor. The real questions are how the site performs on a phone and whether it was designed for the phone first or shrunk down afterwards.
Fluid layouts with CSS grid or flexbox, relative units and media queries (or container queries) rather than fixed pixel widths, plus the viewport meta tag so mobile browsers do not render the page at desktop width and scale it down. Images use srcset and sizes so a phone downloads a phone-sized file. Tap targets need enough size and spacing, and nothing should rely on hover.
Google indexes the mobile version of a page, so content hidden on small screens with display:none is still indexed but should match the desktop content. Test with the Chrome device toolbar and with real devices on a slow connection; the layout can be responsive while the page is still too heavy to use.
<meta name="viewport" content="width=device-width, initial-scale=1"> 