As per dictionaries it means
1. honesty, fairness, or integrity in one's beliefs and actions: a man of honor.
2. a source of credit or distinction: to be an honor to one's family.
3. high respect,
For self it is to be honest in person and a well wisher of every one
Giving Honor to a person is; that you respect one in his/her absence as you respect him/her face to face.
In Islam it is a great sin to say something bad about anyone in absence. On the face, it is also rule that you may not say it in the meeting but you may say it when alone. If you act upon it, you are a honored person and also giving honor to others.