Capacitor relies on each platform's IDE of choice to run and test your app.
iOS requires using Xcode to run your app.
npx cap open ios
Once Xcode launches, you can build/simulate/run your app through the standard Xcode workflow.
npx cap open android
Once Android Studio launches, you can build/emulate/run your app through the standard Android Studio workflow.
Capacitor has a tiny development web server for local testing, but it's recommended to run your web app using your framework of choice's server tools.
npx cap serve
This will open your web app in a local web server instance in the browser.