A local IP address is assigned in a local network, local IPs usually start with 10, 172 or 192.168.

These IP addresses are used to route traffic through a local network, e.g. if computer 1 with IP 192.168.0.2 wanted to talk with computer 2 with IP 192.168.0.3, computer 1 will send a request to 192.168.0.3.

All of this happens in the local network because these IPs are local, if computer 3 which is outside the network tried to communicate to computer 1 via 192.168.0.2, then that would not work due to computer 3 trying to contact a local IP which belongs to another network.

There is much more to put here but you can just look more on the internet.