Final answer:
Horatio refers to the concept that the schemes various characters made in the play have tragically backfired upon themselves, highlighting the theme of unintended consequences of one's actions in Shakespeare's Hamlet.
Step-by-step explanation:
At the end of Hamlet, when Horatio begins to tell Fortinbras what has transpired and mentions "purpose mistook / Fall'n on th' inventors' heads," he is referring to the concept that the schemes of various characters in the play have backfired upon themselves. Horatio has in mind several incidents in the play, such as Claudius's plan to have Hamlet killed in England, which ends with the death of Rosencrantz and Guildenstern instead.
Additionally, Hamlet's own planning leads to the accidental killing of Polonius, which then spurs other tragic events in the play. Horatio's observation underscores one of the central themes of the play: the unintended consequences of one's actions and the way in which attempts to control others can ultimately lead to one's downfall.