“She was promoting her new book.”
You went to a talk given by a business book author last night. You are telling your friend about the event and the speaker. You explain why she gave the talk by saying this.
She was promoting her new book.
To "promote" a creative work means to do things like talks, radio interviews, press conferences, and book signings in order to tell more people about your work. Things that people "promote" include:
promote your book
promote a movie
promote your new album