The Tor Browser tries to hide users from traffic analysis and does so very successfully by bouncing users communications around a network or Tor nodes operated around the world. It is what you use if you want to use the web without being able to be tracked to your physical location.
To use the Tor Browser on KDE neon visit the Tor Browser homepage. Select the Download Tor link at the top and then select the download for your computer. It is most likely you are using the 64bit version of KDE neon so select the Download Linux 64-bit link and a compressed file will download to your computer. After the download has completed, extract the file which should create a new folder (Probably called tor-browser_en-US). Enter the folder and select the start-tor-browser link. You may be asked what you want to do with the file. Select execute to start the browser. It will then connect to the network and you can use it like a normal browser.
Why would people want to do this? Well, there are a host of reasons. Some people just don't like governments and corporations snooping on them and others have very real fears that they will come to harm. Tor can also defeat geo-blocking so it is useful if you want to get around them. I use it to check that my websites can be used by privacy advocates without anything breaking.
For instance if I use Tor to navigate to Mason Bee I can see that my site uses HTML5 canvas data that can be used with other features of my browser to generate a unique fingerprint with which to track my web usage. Tor blocks that by default and asks whether I want to enable it. Making sure that everything works even with HTML5 canvas blocked is something that I want.
If I also look at my server logs to see the computers being served I can see there is an address in Austria currently being served pages. That is me. I am not in Austria but to the web server it appears that I am. To anyone watching at my end I am not connected to the Austrian server but instead to another series of servers on the Tor Network which relay my connections to the Austrian node.