Hoist with his own petard is a Shakespearean idiom. William Shakespeare wrote "hoist with his own petard" in Hamlet. The word "hoist" is the (now archaic) past participle of "hoise", the earlier form of the verb "hoist".
In the following passage, the "letters" refer to instructions written by Hamlet's uncle Claudius, the King of Denmark, to be carried sealed to the King of England, by Hamlet and his schoolfellows Rosencrantz and Guildenstern. The letters, as Hamlet suspects, contain a death warrant for Hamlet, who later opens and modifies them to refer to Rosencrantz and Guildenstern. Enginer refers to a military engineer; the spelling reflects Elizabethan stress.
After modifying the letters, Hamlet escapes the ship and returns to Denmark. By "hoist with his own petar" (literal translation: "cause the bomb maker to be blown up with his own bomb"), Hamlet means he is metaphorically turning the tables on Claudius, whose messengers are to be killed instead of Hamlet. Shakespeare's use of "petar" (flatulate) rather than "petard" may be an off-colour pun.