Middle button emulation provides users with the ability to generate a middle click even when the device does not have a physical middle button available.
When middle button emulation is enabled, a simultaneous press of the left and right button generates a middle mouse button event. Releasing the buttons generates a middle mouse button release, the left and right button events are discarded otherwise.
The middle button release event may be generated when either button is released, or when both buttons have been released. The exact behavior is device-dependent, libinput will implement the behavior that is most appropriate to the physical device.
The middle button emulation behavior when combined with other device buttons, including a physical middle button is device-dependent. For example, Clickpad software button behavior provides a middle button area when middle button emulation is disabled. That middle button area disappears when middle button emulation is enabled - a middle click can then only be triggered by a simultaneous left + right click.
Some devices provide middle mouse button emulation but do not allow enabling/disabling that emulation. Likewise, some devices may allow middle button emulation but have it disabled by default. This is the case for most mouse-like devices where a middle button is detected.
libinput provides libinput_device_config_middle_emulation_set_enabled() to enable or disable middle button emulation. See How do I configure my device on Wayland? and How do I configure my device on X? for info on how to enable or disable middle button emulation in the Wayland compositor or the X stack.