Plain English Meaning
AO2 tells you the weather report was generated automatically by a station that can tell the difference between rain and snow. If you see AO2 in a METAR, no human observer was involved, but the equipment can identify what kind of precipitation is falling.
Full Definition
A code appearing in a METAR report that identifies the weather observation as coming from an automated station equipped with a precipitation discriminator — a sensor capable of distinguishing between liquid precipitation (rain) and frozen precipitation (snow).
Context Anchor
Seen in the remarks section of a METAR, usually near other station-type or sensor information.
Derivation
AO stands for Automated Observation. The '2' indicates the second-generation type of automated station — one with a precipitation discriminator. stations exist too, but they cannot tell rain from snow. The number simply marks the capability of the equipment.