The phrase "to become one's own publisher" means to take on the role of publishing one's own work, rather than relying on a traditional publisher to do so. This can involve self-publishing, where an author pays for the production and distribution of their book themselves, or it can involve using a print-on-demand service to produce and distribute their work. The phrase is often used to describe a shift in the publishing industry, where more authors are taking control of their own work and bypassing traditional publishers.