"Local-first" sounds like a technical term, and it gets explained like one more often than it needs to be. Here's what it actually means, without the jargon.
The one-sentence version
Local-first means the real copy of your file lives on your own computer, not on a company's server with your computer just showing you a window into it.
The difference that actually matters
With a cloud-native app like Google Docs, your document's real, authoritative copy lives on Google's servers. What you see on your screen is a live connection to that copy, which is why it needs an internet connection and an account to work at all: without that connection, there's no file for your screen to show you.
With a local-first app, the real copy is a file sitting in a folder on your computer, the same as a photo or a PDF you've saved. The app opens that file directly. There's no server standing between you and your own words, and no account gating access to it.
Local-first isn't the same as "no cloud, ever"
This is the part that causes confusion. Local-first doesn't mean you can't also have your files backed up to the cloud; it means the cloud copy, if you choose to have one, is a backup of the real file rather than the real file itself. A local-first app's folder can sit inside OneDrive, iCloud Drive, or Dropbox, and those services will sync it the same way they'd sync any other file on your computer, entirely as a byproduct of how your operating system already works, not something the writing app itself needs to know or care about.
Why this matters for a novel specifically
A novel is a project you might work on for years. Over that time, an account-gated cloud app asks you to trust that the company stays in business, keeps the pricing you signed up for, and never locks you out of your own account by mistake. A local-first app doesn't ask for that trust in the same way, because access to your file was never routed through a company's server in the first place. That's the entire idea, not a workaround or a compromise, just a different default for where the real copy of your work lives.
Common questions
Is local-first software the same as offline software?
Closely related but not identical. Offline describes whether an app needs an internet connection to work. Local-first describes where the actual, primary copy of your files lives: on your device, as real files, rather than on a company's servers with your device only showing a synced view of them.
Can local-first software still sync across devices?
Yes, through the same tools you'd use for any files: a synced folder from OneDrive, iCloud Drive, or Dropbox. The files themselves are still the real, primary copies; syncing just means a second device also has an up-to-date copy of them.