How do you make all your links stay on the homepage, just different content?

Hi, I'm working on my site and had a question I was wondering if people could answer.

I want to make it so that you have your homepage, and then there are links at the top.  Currently, the links connect you to different pages.  But I want it to be so that when you click on the link, you stay on the same homepage (background image and everything is the same), but just the text changes.  You stay on the homepage, just there's different content.  Does that make any sense?  I know this is a pretty common thing in web design, but what would you call it, and can you do it on Square Space?  Would appreciate any help so much.  Thank you, and hope to hear some thoughts soon!

Those are anchor links and how they work depends on your site and template.