A responsive web design provides the flexibility for its use with multiple devices. Responsive designs do not assume what the width of a browser window is, and adjust to devices bearing both portrait as well as landscape modes. No web design, however, can be scaled effortlessly beyond the limits of its original framework. 

The term commonly used for this type of design is "Responsive Web Design". The content that exists on your standard web pages needs to be viewable and accessible via today's mobile devices. That means that the information may actually reorganize on the page to accommodate the width of the particular device. It also means that it must remain readable.

If you browse to your website from the browser on your smart phone and you see the full site on your phone and you have to pinch and tweek to be able to read the content, your website is NOT mobile friendly. Websites on a phone read in an up and down scrollable window and should never exceed the width of the device (you should never have to scroll left to right).

Does your site pass Google Mobile Friendly test? You can check here:

https://search.google.com/test/mobile-friendly

Note: passing this test might not be enough. Many sites use a mobile site redirect off of the home page but the inside pages of the site are still not responsive. If Google detects this, your entire site will be diminished in the search results.