What is the meaning of implication?

noun

• Something that is inferred (deduced or entailed or implied. )
  • usage: "his resignation had political implications"
  • synonyms: deduction, entailment
• A meaning that is not expressly stated but can be inferred.
  • usage: "the significance of his remark became clear only later"; "the expectation was spread both by word and by implication"
  • synonyms: significance, import
• An accusation that brings into intimate and usually incriminating connection.
• A logical relation between propositions p and q of the form `if p then q'; if p is true then q cannot be false.
  • synonyms: logical implication, conditional relation
• A relation implicated by virtue of involvement or close connection (especially an incriminating involvement. )
  • usage: "he was suspected of implication in several robberies"