To run a spring boot application, you click the button when you have your main class (class with main method) in focus. However it is not so often I got this open, so you can set the IDE to run it automatically when you press run. Here is how.
Click on the button in the top stating "current file" and select the option "Edit Configurations..."
Press the "+" button and select "Application", to make a new application configuration.
Give your run configuration a name and then click on the main class field, to select your main class.
Select you main class and press ok to all dialogs.
You can now press the run button or use the shortcut keys to run your application.