Resultative compound: 烧 (to burn) + 光 ('to nothing, completely used up'). 光 as a result complement often means 'to zero / exhausted' - compare 吃光 (eat it all up), 用光 (use up), 花光 (spend all). Different from the homograph 光 'light/bright'.
history
The phrase carries strong wartime resonance from the Imperial Japanese Army's 三光政策 ('Three Alls Policy'): 烧光、杀光、抢光 - burn all, kill all, loot all. Any Chinese reader recognizes the verb 烧光 partly through this historical association.
