From 'a big pile of work' to a path with a position on it
Imagine someone hands you a goal like 'renovate the kitchen' and nothing else. That's not something you can pause and resume in any meaningful way, because there's no notion of where you are inside it. Did you make progress today or not? Nobody can say, because 'renovate the kitchen' isn't a position, it's just a pile. Now compare that to a plan: remove old cabinets, then rough in new plumbing, then install cabinets, then countertops, then paint. Each item has a place in a sequence. At any moment you can point to exactly one step and say 'I'm here, this is next.' That single sentence, 'I'm here, this is next,' is what makes a multi-week task manageable at all.
This is what goal decomposition means for long-horizon agents: taking one large, vague-sounding objective and turning it into an ordered list of concrete sub-tasks. It's not enough to just list the pieces of work, order matters, because order is what gives the agent a current position. Without ordering, resuming a paused task is guesswork: the agent would have to reconstruct what's probably done from scratch every time. With ordering, resuming is trivial: check which step is marked current, and start there.