In the language of intelligence work, an agent who is burned has been exposed and is useless — their cover is gone and they cannot be sent back.
The word is the past participle of burn doing duty as an adjective, and it has several other lives. Burned or burnt describes food ruined by heat, and skin reddened by sun. Burned out means exhausted past recovery, of a person or a light bulb. And burned as a slang term means humiliated by a sharp remark. Note the British preference for burnt as the adjective and burned as the verb, and that American English uses burned throughout.
1adjectiveburnedOf an agent or source, exposed and no longer usable.
“Once you are burned there is no going back in.”
2adjectivedamagedDamaged or destroyed by fire or heat.
“The whole top floor was burned out.”
3adjectiveexhaustedExhausted past the point of recovery.
“He was completely burned out by forty.”
Too few real examples of this word to estimate which sense is commonest.
Middle English
burnede
English, today
burned
The past tense is inherited from Middle English burnede. The past participle (from which the adjective is also derived) is inherited from Middle English burned. Synchronically, both forms are equivalent to burn + -ed.
Etymology from Wiktionary, CC BY-SA