A series is a collection of books that share something significant in common. In fiction, the commonality is usually characters, a particular conflict, or setting.
Some series allow the individual books to function wholly independent from one another. They don’t connect in terms of plot, so you can jump around in the series and not lose track of the story or miss out on important elements. These are like a trip to the ice cream parlor. Each flavor is a different delight, but you know you're getting something you like—ice cream—in every serving. Arthur Conan Doyle's Sherlock Holmes books are an example of this.
Other series have an interlocking structure where the books inform one another in a more fundamental way. While each book is complete in and of itself, you usually want to read them in order, as events that happen in one book are important to those that happen in the next. J.K. Rowling's Harry Potter series falls in this category.
There are more specific kinds of series as well, such as the trilogy, which is a series of three books. Each book is complete on its own, but together they tell a larger story.