So basically, a Lightning Component framework is a UI framework for developing single page applications for mobile and desktop devices.
What is the meaning of single page applications here?
A single-page application is an app that doesn't need to reload the whole page during its use and works within a browser. So basically you reload the specific section of the page when needed instead of reloading the whole page. This reduces the effort to reload the sections which do not need to be reloaded. You stay on the same page.
The goal is faster transitions that make the website feel more like a native app.
Example: Imagine you are filling the online form for a job application which has several sections and each section has different set of fields to fill. When you fill the one section and click next, the next section renders without reloading the whole page and you stay on the same page until you fill the whole form. Also, you can move back and forward until you submit that.