A "personal apology" means expressing regret for something you did or said, directly to the person or people you affected, and accepting responsibility for your actions. Full definition
Under the leadership of President and Chief Baking Officer Bobbie Lloyd, the company trains its staff to frost cupcakes the Magnolia Way, continues to refine founder Allysa Torey's original recipes (check out The Complete Magnolia Bakery Cookbook), and emails personal apologies to the rare customer who has a bad experience with its counter staff. (entrepreneur.com)
Despite an immediate personal apology to Mrs Duffy, it was widely seen as a career - ending moment. (news.bbc.co.uk)
Immediately after the guilty plea, Metropolitan police commissioner Sir Bernard Hogan - Howe issued his first personal apology to Mitchell. (theguardian.com)