Most novels are one-offs -- ie. a single story contained within a single book. But sometimes the writer -- or publisher -- feels there is more story to tell. Enter duologies. Basically that means sequels and prequels. A sequel is a continuation of the original story, and a prequel is the setup of events preceding and leading up to the original story. A prequel can obviously be read and enjoyed on its own merits, but a sequel is trickier. It has its own plot, but it builds off the original book, which means new readers can be satisfied with the story but will probably have questions about that first book. It's inevitable. The Truths I Learned From Sam and In Search of Sam (Dundurn Press) are an example of a book and a sequel. Though the sequel can be read as a stand-alone, for full enjoyment it is preferable to read both books -- in order. If you read In Search of Sam first, I'm sure you'll like the story fine, but it will be a spoiler for the first book.
A book series is a different kettle of fish. Consider the old Nancy Drew novels. The main characters are the same in every book, but the mysteries are different. Consequently the books can be read in any order, because the stories stand alone. This is called a formulaic series. My Zach and Zoe books (Lorimer) are an example of this.
And then we get to trilogies and other longer serialised book sets such as Harry Potter and The Hunger Games. These are called meta-narratives, which means they have a single storyline running through all the books in the series. Though each book has its own plot and storyline, there are overarching elements such as theme, recurring characters and settings, protagonists, antagonists goals, obstacles, etc. which link all the books together.
And therein lies the answer to the question: Should the books of a trilogy be able to stand alone? Not really. That is not the intention. The second book grows out of the first and the third out of the previous two. In fact, the first book(s) usually foreshadow upcoming events in the subsequent books. Threads get carried forward. For the full experience, a reader needs to read all the books in order. The fact that they're connected is what makes them a trilogy.
trilogy -- a group or series of three related things
Certainly the author reminds readers of noteworthy details from the previous books to jog their memories, but there shouldn't be any info dumps. Each book in the trilogy has its own storyline, so it feels complete when the reader finishes the book, but it is still part of the larger all-encompassing storyline which doesn't get resolved until the trilogy ends.
Consider Lord Voldemort (sorry, I mean 'He who shall not be named" -- HWSNBN) in the Harry Potter books. He makes a pest of himself in every book, and we are constantly learning new information about him. We know he is Harry's mortal enemy and we know it's eventually going to come down to a battle between the two, but we also know that battle won't occur until the last book of the series. That struggle is the big storyline running through the entire series. In the meantime, every book has its own storyline to carry the reader along. The point is JK Rowling doesn't retell every fact about HWSNBN in each and every book. She allows our knowledge of him to grow, not repeat like heartburn. And that is how it should be. Readers get cross if you waste their time with stuff they already know, and they will know it, because they will have read all the books -- in order. No one reads the Deathly Hallows first!
So please don't try to read The Bridge of Whispers without first reading The Druid and the Dragon. I would love for you to read them both -- and then The Sorcerer's Revenge after that, but all in the right order.