Professional communication is the writing and speaking you do at work for clients, colleagues, or the public, rather than for friends.
Email a customer about a delayed order, or brief your manager on a project; that counts. Texting a buddy about weekend plans does not.
A nurse phoning a patient's family to explain a change in medication times is doing professional communication. She picks calm, plain wording, confirms the details, and stays respectful, because she is speaking for her workplace to someone she may not know.
A shop owner emailing a supplier to say a delivery arrived damaged also counts: the message is in the writer's work role, aimed at a business contact. The same owner venting about the damage on a personal social media page would not be.
In short, it is the work side of your words, shaped for the audience and the job at hand.