When you’re mired in something, you’re stuck or entangled in it. You can’t get out.
Sometimes, being mired means to be literally trapped in the mire, which is like a swamp or muck. But usually when people are mired, it’s in something less icky but equally hard to get out of. You could be mired in six hours of homework. Congress could be mired in discussions that are going nowhere. A bad relationship could be mired in arguments. When you’re mired, it feels like you’re sinking in quicksand.