QuickTime Player does a decent job of screen recording with microphone audio on Mac system. Listed below are steps to do screen recording with audio using QuickTime Player.
Step 1: Launch QuickTime Player then click File menu and select New Screen Recording from the menu list.
This should display the following Screen Recording App.
Step 2: Click the arrow pointing downwards on Screen Recording App and select Built-in Input: Internal microphone from the drop-down list. By default Microphone option is set to None.
If you want to display the mouse clicks the select Show Mouse Clicks In Recording.
Step 3: After selecting the above mentioned options, click Recording button on Screen Recording to start video capturing of the screen with audio from Microphone.