The .local top-level-domain (TLD) is reserved to be used for your LAN. Every machine has its own hostname, and if configured properly, it is accessible on your LAN by the name of hostname.local.

There are two competing standards, mDNS/multicast DNS and LLMNR; both use the same principle of listening to broadcasts. Basically, when a computer needs to resolve foo.local to an IP address it will perform a broadcast query on the LAN; the foo machine will then respond to the broadcast with an answer which contains its IP address. mDNS is primarily used by Linux, LLMNR is used primarily by Windows. I’ll focus on mDNS.

In order for this to work, you need two things:

1. mDNS needs to be enabled on the client machine that’s trying to resolve foo.local to the IP address.
2. The foo machine needs to listen to the mDNS query broadcasts.

For 1. you can run ping from command line, to check whether the machine is discoverable. For troubleshooting see Linux DNS on how to configure Linux client-side DNS resolution.

For 2. simply make sure that avahi-daemon is installed: sudo apt install avahi-daemon. After the daemon is installed, it immediately starts responding to broadcast requests.

Troubleshooting

Verify that avahi-daemon is actually running:

$ ps -ef|grep avahi-daemon
avahi     104107       1  0 12:56 ?        00:00:00 avahi-daemon: running
avahi     104119  104107  0 12:56 ?        00:00:00 avahi-daemon: chroot helper
$ systemctl status avahi-daemon

In my case, avahi was not running, and it suddenly sprung to life after I run systemctl status avahi-daemon… wtf systemd?

In case of host name conflict, avahi adds the -2 suffix to the host name; you can verify that by ping/ssh machine-2.local. If that works, browse the logs via journalctl -u avahi-daemon and search for the “Host name conflict” line. You can try a bunch of tips from this archlinux forum, e.g. disable ipv6 for avahi, or just restart avahi-daemon via systemctl restart avahi-daemon.