Metered and unmetered Wi-Fi refer to how data usage is charged or limited.
A metered Wi-Fi is a monitored connection with a limited amount of data available for usage on a device. Going over the limited amount results in having to pay additional fees. Metered connections are commonly provided by ISPs for homes and businesses.
On the other hand, unmetered Wi-Fi means that the amount of data that can be used is unlimited, and the charges are fixed and unrelated to usage. Unmetered connections are usually provided for free in coffee shops, airports, and other public places.