"Add to Home screen" is a feature available in modern browsers that allows you to "install" your progressive web application as a standalone app.
How to install the web app?
Follow the guidelines for popular platforms:
Safari on macOS Sonoma: open the web app, press File > "Add to Dock..."
Safari on iOS or iPadOS
Google Chrome on computer or Android.
Starting with iOS 17.4 in EU countries, web app cannot be added to the home screen due to Apple's decision.