Public speaking is intentional human-to-human communication.
When we have a message to get across, whether it is developed beforehand or developing as we go, we have intention behind our words. When we have compelling intention we are more interesting and people want to listen. The instant someone stands up in front of a group, be they a politician or standup comic, the audience expects that person to have something important to say. To be a dynamic act, public speaking must be intentional.
"Human-to-human" means speaking is not limited to formal, public settings with lots of people. It can be that, but when we open up our definition to be 'anytime, anywhere, with anyone', we start to open up to all of the methods and dynamics available to us. Speaking happens constantly with friends on the phone, family in the car, and coworkers at lunch. Learning to communicate naturally in multiple human dynamics is a skill-broadening endeavor.
And consider the modes in which the public speaking can occur. It can be live or prerecorded, on phone or video, amplified or organic. But although the available delivery modes have increased since its earliest documented teachings thousands of years ago, the one mode that has remained constant is the actual act of speaking. Mimes are still not considered public speakers.
In addition to verbal communication skills, public speaking uses visual skills (body movements, graphics, and use of props), and physical skills (engaging the audience in physical activities or purposeful movement during the presentation).
Regarding the word "communication" in the definition, although most presenters do not view public speaking as dialogue between the presenter and audience, it can be useful to approach presentations as conversations rather than monologues. (This becomes more difficult as group size increases, i.e. forget interactive conversation with a stadium full of people.) Pose interesting questions to your groups, elicit responses, and consider what they say in return. Allow yourself to engage people in short conversations if your mind is so present. The Politician Speech where one waits until the end of their monologue to ask for questions is boring as spit. Avoid it unless you are a celebrity or giving fire drill instructions.
Expanding our definition of public speaking lets us more frequently practice our skill sets in varied dynamics, more comprehensively honing our communication ability. How often can you allow yourself to be your most engaging, emotionally resonant, and clear with your communication?