Can anyone explain to me, in the simplest possible terms, whether it is possible to create/edit and host a SQL database locally on my PC? I've so far managed to run PHP locally using XAMPP, but have been at a loss as to how I could implement SQL locally too.
For example, can I download phpmyadmin directly to my PC and use it to implement database features on my website without having to be connected to the internet?
It's possible. And you don't need to download any other software.
Fire up XAMPP and start the Apache and MySQL servers then go to your browser and enter http://localhost/phpmyadmin.
Once your MySQL server is up, you can easily access it from applications running locally with the necessary configuration (i.e host, username, password, port etc).