Plain English Meaning
The worst weather you are still legally allowed to fly in. If the weather is below these limits, you are not allowed to fly that flight under those rules.
Full Definition
The lowest weather conditions — typically expressed as visibility and cloud ceiling — under which a pilot is legally permitted to operate an aircraft under a given set of rules (such as VFR or IFR) or for a particular flight operation, airport, or pilot certificate level.
Context Anchor
Used during flight planning, go/no-go decisions, training lessons, and risk management before and during a flight.
Derivation
Minimum comes from the Latin minimus, meaning smallest or least. So weather minimums are the least weather conditions — the floor below which flight is not permitted.