The noun meaning "premature ignition in an internal-combustion engine" is recorded by 1897. As a verb, of schemes, plans, etc., "to affect the initiator rather than the intended object" it is attested from 1912, a figurative use from the accidental back-firing of firearms.
1975, transitive, "start up (a computer) by causing an operating system to load in the memory," from bootstrap (v.), a 1958 derived verb from bootstrap (n.) in the sense of "fixed sequence of instructions to load the operating system of a computer" (1953).
This is from the notion of the first-loaded program pulling itself (and the rest) up by the bootstrap. The intransitive use, of a computer operating system, is from 1983. Related: Booted; booting.
former transliteration of the name of the Chinese capital city, now (in the pinyin system) called Beijing. In the Wade-Giles system it was Peiping; the form Peking pre-dates Wade-Giles and was formed by the old British-run, Hong Kong-based Chinese postal system. Peking duck, "large domestic duck of white plumage and orange beak and legs," is attested from 1880.