Icons a web app manifest needs
Browsers that install web apps read the icons listed in the manifest. Chromium-based browsers look for at least a 192 pixel and a 512 pixel icon, used for the home screen, app launcher and splash screen. The zip includes icon-192.png and icon-512.png for those, plus apple-touch-icon.png at 180 × 180, because Safari has long used the apple-touch-icon link for home screen icons.
What a maskable icon is
Android displays app icons in whatever shape the device uses, such as a circle, squircle or rounded square, by cropping the image. A regular icon can lose its edges in the process. A maskable icon is designed for this: its important content sits inside a central safe zone, a circle whose diameter is 80% of the icon, and the rest is filled with background.
maskable-512.png is built that way. It adds an extra 10% of padding per side on top of your padding setting, skips the corner radius because the device applies its own mask, and fills the background with your chosen color or white. In the manifest it is listed separately with purpose set to maskable, so devices that don't mask icons use the regular ones.
Adding the icons to your app
Copy the PNGs to the root of your site; the paths in manifest-icons.json point to /icon-192.png and so on, so edit them if you use a different folder. Merge the icons array into your manifest alongside name, short_name, start_url and display, and link the manifest from your HTML. The same array is shown on the page with a Copy button. After deploying, the Application panel of the browser developer tools lists the icons it found in the manifest.