The term "local network" refers to the set of computers and devices that can be reached directly from your computer without going through the Internet.
For example, your home router, your network printer, or the intranet of your company are usually on your local network, also called LAN for Local Area Network. In technical terms, this refers to the set of IP addresses defined in [RFC1918](https://tools.ietf.org/html/rfc1918), like IP addresses that start with `192.168`.
Accessing resources on the local network can be useful in the context of Tails, for example to exchange documents with someone on the same local network without going through the Internet.
But an application that can connect to both resources on the Internet (going through Tor) and resources on the local network (without going through Tor) can deanonymize you.
This page describes some of the security measures built in Tails to protect from such attacks and explains how to access some types of resources on the local network.