(Comes from the code of honor that Samurais of China and Japan followed, comparable to the code of Chivalry that European Knights upheld)
to accept and treat as valid (to honor a debt),
to grant as a privilege (I'm honored by your company),
to respect or pay homage to (the statue honors WWII veterans).
As a noun: A significant part of one's dignity or value (I will defend my honor),
the respect or distinction payed to someone or something (it's an honor to win this award),
something given or used to show respect, status, achievement, or deference (the title "your eminance" is purely honorific) or a title thus purposed (always address the judge as "your honor")
A feminine given name, originating from a hope to bestow a child with certain qualities by invoking those qualities with a name, such as love, faith, hope, charity, chastity, etc.