In my story, I realized I hit a derivative, bland dead end with a creature I introduced. When my plot screeched to a halt and my characters were treading some seriously unnecessary and whimsically-inappropriate literary water, I realized that my train-of-thought had completely derailed. I've had trouble reconnecting since then.
I can't even call it writer's block. I just felt so dumb for thinking that any of that huge block of prose mattered. It was suddenly bedtime. I slept in a haze of stupid and woke to the bright early sunlight of enlightenment... I think! I think the tangent-purge is important to figuring out what actually matters in the story, and what will never matter. And when I'm ambling along at a snail's pace with no deadline to keep me true to the story, that's fine. But here there be deadlines! The rule is that you get to cut out whatever doesn't advance the story. But that's for the Editing Phase!
I realized that I used my tangent to develop missing traits in my characters. I was searching for the defining psychological features that would connect them with the audience, make them sympathetic and worthy of caring. I explored their habits and vices a bit more. I did this for the sake of the story. Now that I "know" my people better, they'll "act" more naturally and true-to-self even when all the crap is cut out. Otherwise, the remainder of the story would be hollow in some way, just a string of facts.
In Christopher Pike's Remember Me, the main character is a ghost who, when alive, constantly broke her hairbrush handle when brushing her hair. (I was confused until I started to do this myself. It just happens!) Anne McCaffrey's Robinton has a penchant for fine wine and Menolly is too tall and lanky for a proper girl; Anne Rice's Ramses eats delicately without ever touching his food to his lips and Louis shuffles his feet in a very human fashion. In a Jane Lindskold novel, the main character speaks only in literary quotes and converses with inanimate objects. Stoker's Dracula has blond hair and a heavy handlebar mustache.
These are all random details and mannerisms that are burnt into my memory. They reveal everything and nothing about the characters who exhibit them. How do authors burn in such random details? Maybe it's the result of a tangent. Well, if Peter Pan can sleep on his way to Neverland because he's now light as the air, then Lancelot is physically ugly but charismatic because he's so dang chivalrous. Arguably, it's the fault of those stupid top-hat nests made by Never-birds...
And I learned about horcruxes and the like from Elric long before Harry Potter tried to corner the market...
See? A tangent. Welcome!