Plain English Meaning
The part of the aircraft that normally generates electricity has quit working, so the aircraft is now running only on what's left in its battery.
Full Definition
A condition in which the aircraft's alternator stops producing electrical power, leaving the battery as the only remaining source of electrical energy for the aircraft's electrical systems.
Context Anchor
Seen during instrument flying when a warning light, electrical gauge, or loss of electrical equipment shows that the charging system may not be working.
Derivation
Alternator comes from the Latin alternare, meaning 'to do by turns,' because the device produces alternating current. Knowing this helps why the failure of one , component can take the entire charging system offline.