When an author self-publishes, they finance the publication of their own book. This means that the author pays to have the book edited, designed, printed, and distributed, rather than seeking out a traditional publishing house to do those things.
There are many reasons why an author might choose to self-publish. They may have had trouble finding a publisher for their book, or they may want more control over the publication process and the final product. They may also want to retain the rights to their book, or they may want to get their book out into the world more quickly than traditional publishing would allow.
Self-publishing is a great option for many authors, but it does require a certain level of knowledge and skill. The author will need to be able to market and sell their book effectively, and they'll need to be comfortable with all aspects of the publication process.