A traditionally published author is one who has a book published by a mainstream publishing house. Traditional publishing involves an editor working closely with the author. Publishers usually offer authors an advance against future royalties, and provide editing, design, marketing, and publicity services to make sure the book reaches as wide an audience as possible.
Traditional publishing can require a more involved process than self-publishing. Generally, an author will have to submit a query letter and sample of the work to publishers and literary agents, who then choose which works they would wish to represent and pitch to a publishing house. Once accepted by the publishing house, authors need to work closely with editors to finalize the book and develop a marketing plan for it.
Compared to self-publishing, traditionally published authors have generally more access to resources and professional industry knowledge. Traditional publishing also offers more recognition, with the possibility of having their books sold in bookstores, and having their work reviewed in newspapers, magazines and websites.
On the other hand, traditionally published authors generally have to relinquish some control over the final product, share profits with the publishing house, and may have to wait much longer for their book to be published.
If you are interested to know more about the differences between traditional and self-publishing, you can find some helpful information here:
https://www.thebalancesmb.com/difference-between-traditional-and-self-publishing-1003544.