It is an old and outdated expression. It's used nowadays only as a joke, much as someone might say "Prithee, fair maiden, woulds't hie with me to yon Dunkin' Donuts and quaff a flagon of coffee?" It would typically have been used when a man and a woman, in a sexual relationship--perhaps living together--got married, perhaps because the woman had become pregnant. The societal view was that the relationship was sinful, and especially shameful to the woman. But if the man "made an honest woman" out of the woman by marrying her, society could forgive and forget. I _think_ "honest woman" did not mean "truthful." I think a prostitute would have been a "dishonest woman" and a married woman would have been an "honest woman."

"make an honest woman (out) of" is a dated expression - people don’t say it any more, unless it’s meant humorously. It means to marry a woman you are having a sexual relationship with , especially to avoid scandal if she is pregnant. sources: http://dictionary.cambridge.org/dictionary/english/make-an-honest-woman-out-of-sb https://en.oxforddictionaries.com/definition/make_an_honest_woman_of

to make an honest woman [out] of sb = to marry sb The idiom comes from the old-fashioned idea that it's immoral for a woman to be in a romantic relationship before she is married. It is still occasionally used today as a joke, therefore it doesn't necessarily imply that the speaker has old-fashioned views about romance. (Still, it's not that common these days)

I bet her father was happy to see that you made an honest woman of her. ~ He raised her up to his standards of what he considers a decent person. (honesty, integrity, etc)