Local-first generally refers to apps that work with a local client database which syncs with a server database in the background. Reads and writes go to the local database first. This results in very low latency and not being dependent on the network for working with data. The term is often applied loosely and architectures and implementations differ quite a bit.

This community has been central to the idea of local-first: https://localfirstweb.dev/

The term local-first was coined by Martin Kleppmann et al in this essay: https://www.inkandswitch.com/local-first/