Welcome to the forums ! Which part of this project is it that you're wanting an explanation on? If you're just starting out and the button presses are a mystery I suggest you run through some introductory videos which will help you get the basics - this series by Jeremy Blum
If it's the menus that are baffling you, you'll probably find the Switch & case
statements of interest. It sounds like a very simple menu system so you'll find lots of entries on this forum with examples, and talking about libraries that can assist if you search for "LCD Menu".
Cheers ! Geoff