Have you ever been watching a movie or reading a book in which a character does or says something that doesn't fit with who that character has been set up to be, and you're left annoyed, wondering why the character behaved or spoke as such? And then the plot continues cranking right along, and if the story's very funny or involving, or there are lots of explosions and cool special effects, you keep watching or reading, but with lower expectations. This is what happens when plot drives character, instead of the other way around.
A common example of this problem is the story that would never get off the starting blocks at all, were it not for some illogical action on the protagonist's part. Otherwise level-headed and pragmatic CPA Polly suddenly decides to ditch the security and status she's come to love in her career, move to the other side of the country and open a cupcake shop---not because she's always yearned to be more of a free spirit, dreamed of being a professional baker, has always wanted to move far away, or any other good reason based in logic or her life cicumstances, but because doing these things will open the door to a series of madcap adventures and romance with a cute industrial restaurant supply sales rep who lives in the new city.
You might wonder why the author doesn't just start the tale in the new location, with Polly getting settled in and looking for a good retail bakery space. The author thinks, in beginning with Polly's 'old' life, he's setting up the necessary background to create a "fish out of water" story and demonstrate an arc of character growth. But in reality, unless there's some very compelling reason for Polly to uproot herself in this way, her behavior and choices read more like authorial convenience than growth.
Perhaps even more annoying is the character who's been well-established, whom you've come to like and root for, right up to the point he does something that makes no sense whatsoever. Suddenly, this fully-realized, three-dimensional person becomes a puppet on a string, being forced to go through certain motions to get the reader or viewer to the next major plot point.
In a thriller, the sweet, kind, but mousy library clerk who's normally scared to walk to the parking lot alone at night nevertheless ventures into the dark basement alone when he hears a strange noise from the top of the stairs. In a sci fi novel, the by-the-book researcher who finds his lab has been breached doesn't report it to the proper authorities, but decides to launch his own, private investigation instead. In a romance, the strong-willed, self-sufficient, feminist heroine melts into a needy puddle of damp lace doilies at the sight of her beloved. In a mystery, the clever and resourceful hero could resolve a case of mistaken identity with a single phone call to one person, yet somehow the idea never occurs to him. I could go on, but do you really want me to?
The reason why this is so irritating to the reader or viewer is that our estimation of a story's believability is based on how well it jibes with our own, real-life experiences and knowledge. Even in a fantasy or sci fi story, we want the behavior of human and humanoid characters to match up with what we know of real-life people. And in real life, character ALWAYS drives plot.
Every choice that every real person makes every day is a product of who that person is. His motivations, goals, fears, desires, etc. are all rooted in his background and lifetime of experiences to date, and it's his motivations, goals, fears, desires, etc. that dictate his actions.
The cure for the author-as-puppeteer syndrome is to begin with well-drawn characters, and then keep asking yourself, "Given who she is, what would this character do when confronted with these circumstances?" as opposed to, "What does this character need to do or say to get the story to the next major plot point?" Even in an intricately-plotted novel, characters should never act...well, out of character.
I tend to start with a character and a set of challenging or unusual circumstances, and let character dictate plot. Whatever I believe the character would do next is exactly what happens. If you're going to begin with plot, then you probably need to work backward: rather than creating the character and then asking yourself what she needs to do or say to get to the next plot point, start with an assumption that the character is going to do or say whatever is necessary for the sake of plot, then ask yourself what kind of character would do or say that thing. In so doing, you create the illusion that character is driving plot.