When "honest" came into the language from French, in the 14th century, it had the general meaning of "held in honour, honourable, respectable". A century later it had developed its modern sense, often to be found in Shakespeare. But the older meanings were still around. The meaning of "honourable" can be heard when Hamlet describes himself to Ophelia as "indifferent honest" (Hamlet, III.i.122) or Antony describes Brutus as "noble, wise, valiant, and honest" (Julius Caesar, III.i.126).
The word means "genuine, real" when Hamlet describes what he has seen as "an honest ghost" (Hamlet, I.v.138). And it means "innocent, well-intentioned" when Hero talks about devising "some honest slanders To stain my cousin with" (Much Ado About Nothing, III.i.84). But the most important difference from modern English is the sense of "chaste, pure".
When Touchstone says to Audrey, "thou swearest to me thou art honest" (As You Like It, III.iii.23), or Othello says to Iago, "I think my wife be honest" (Othello, III.iii.381), they are not enquiring into their women's truthfulness, but their morals.