Plain English Meaning
Working out how heavy the aircraft is with everything loaded, and where that weight sits along the aircraft, to make sure both are within the limits the manufacturer says are safe.
Full Definition
A required preflight calculation that confirms an aircraft's total loaded weight is within certified limits and that the center of gravity falls within the approved forward and aft range for safe flight.
Context Anchor
Pilots encounter weight-and-balance before flight when planning fuel, passengers, baggage, cargo, or training scenarios that test safe loading decisions.
Derivation
Weight comes from an old word meaning heaviness. Balance comes from an old idea of a two-pan scale. Together, the phrase points to the two checks that in : how much the aircraft carries and how that load is arranged.