For me, novels are a way to escape into a fantasy world and take a break from my real life. Picking up a book from a series is appealing for many readers because of the comfort provided by familiar characters, settings, or writing. When I already understand who the characters are and what they have been through, I appreciate their future struggles even more.
Novels allow the reader to watch the main characters learn, grow, and face the challenges in their lives. A series can show far more of this development than a stand-alone novel ever could. Relationships can be built and crumble without feeling like they are forced, or each character can have their own moments to overcome their weaknesses.
While they may just be words on a page, these characters can become real friends to the imagination. Many people wonder what the future lives of their favorite characters will be, or write future stories themselves through the medium of fan fiction. Reading a book series is appealing because you can discover more of what the characters are going to face in their lives and see that they live happily ever after.
Book series also provide a comfortable familiarity. While the plots are different and the characters grow and change, readers will generally find that the writing style or main themes remain the same. Despite any plot twists, they know what to expect when they pick up a book in a favorite series. To some people this may sound boring. However, to me it is a great blessing to find something joyful that I know I can count on for an escape from the moment.
Many authors find themselves far more knowledgeable about the lives of their characters than is necessary to write a single book. They may be able to clearly picture what other adventures they will find themselves on. Writing a book series gives the author a chance to share these other stories, without doing additional world building or developing many new characters.
Publishers can be leery of first time writers who approach them with a series because they do not want to obligate themselves to print more books if the first one does not find an audience. However, after an author is established a series is a huge plus. Readers will want to purchase the next book to see what happens in future installments and the audience will grow.
There will always be pitfalls for authors who write series. They may not end them in time and find the writing suffers, or they may feel pressure to continue after they want to finish it. But for readers, a book series is an appealing way to spend their leisure time. Reading the latest novel is a way to visit with old friends and explore your imagination.