You are not alone if you don't know how to tell if a website is responsive or not. There are plenty of people who still don't know what a responsive website is or how to tell if a website is responsive.
It's ok for developers like us who know and understand the jargon of responsive websites, but we want you to know and understand too. In a nutshell a responsive website is a website that responds to the size of the device you are viewing it on, i'll explain it in a little more detail below.
Is an approach to web design aimed at allowing desktop webpages to be viewed in response to the size of the screen or web browser one is viewing with - Wikipedia
If you look at a website on a mobile phone in portrait view and landscape view the site will look different, it doesn't mean it's a different site it means the site is responding in a different way to the phones width and adapting to the size of it and displaying it in a different manner.
A good graphic that explains what responsive is, is the one below. Your responsive website is like water it takes the shape of the object it's viewed on.
Ever wondered why you have that icon of 3 horizontal lines for the menu? this is because there isn't enough width on a smaller devices to display the full website menu that you see on the desktop version, so this icon that users tap to expand to see the menu is used instead.
You may of heard of it as making your website 'mobile friendly', this is because of the ever growing mobile phone using population, and internet users on mobile devices now overtaking those who browse daily on their desktops. This also resulted in Google now listing mobile friendly sites first in their search results, so to not miss out on potential visitors to your site you should make sure you website is responsive.
User experience is a big thing to website users, if your website is hard to navigate, not clear and not mobile friendly you will be missing out on potential customers and even more worrying sending them elsewhere.
So next time someone asks do you know what a responsive website is, you can nod clearly with confidence and even tell them you know how to tell if a website is responsive or not.
Or if you are still unsure or want to have a chat to discuss this further please contact me firstname.lastname@example.org