Usually .local names are resolved using mDNS – the Linux servers probably run Avahi, OS X has it built in, and for Windows there is Apple's own Bonjour.
2020-12-14: Updated for Windows 10 built-in mDNS support.
Windows 10 (version 1511 or later)
Windows 10 handles both hostname and hostname.local identically: it simultaneously tries LLMNR for the bare hostname, NetBIOS for the bare hostname, and (optionally) mDNS for hostname.local. This mDNS support is not restricted to 'Modern' apps anymore.
In current versions (somewhere around 10.21xx or later), I believe mDNS hostname lookup support should be active by default.
Originally, in older versions (10.1511 or later), mDNS support had to be activated manually by setting the EnableMulticast registry value to 1:
reg add "HKLM\Software\Policies\Microsoft\Windows NT\DNSClient" /v EnableMulticast /t REG_DWORD /d 1 /f
Windows XP—8.x
An older version of Bonjour (v2.0) is included within Bonjour Print Services. It is also available as a Chocolatey package.
The latest version (v3.x) is not available as an independent download, but is installed as part of iTunes (and a few other applications). It is possible to use an archive manager (like 7-Zip or WinRAR) to extract Bonjour64.msi from the iTunes installer.