Is it a large seamless novel chopped up into several parts, or is it a collection of independent novels with recurring characters?
A series is a sequence of related works under the same title (individual works/books/episodes can have their own names).
A TV or novel series can be chronological pieces of the same story (Battlestar Galactica, Harry Potter). Or it can be completely separate stories under the same umbrella (Twilight Zone).
A series can have a planned ending (Discovery of Witches) or it can continue forever (as long as there is funding and a will to produce or publish it, otherwise, it might get an ending, or just stop) (every soap opera ever, Star Trek).
In indie publishing, it's the same thing, except a series probably won't be planned to go on forever. A comic series is generally "the continuing adventures of..." And a book series might be a trilogy or more.
Then there is a serial, which is the subset of a series where there is progression in characters and chronology, as opposed to being stories set in the same universe. To serialize a work means to break it up and publish one piece at a time.