What does the orange dot next to the app on my iPhone mean?

The orange dot indicates that you installed a beta version of the app, usually installed via the app "TestFlight".

TestFlight is an app from Apple that must be used for beta testing. A quote from Apple: "After you download the beta app, you will see an orange dot next to its name that marks it as beta."

The full instructions for beta testing with Apple can be found here: TestFlight - Apple.