This character is someone of honor.
A honorable character acts in accordance with principles of honor, with dignity, distinction, and an illustrious, noble and distinguished way.
There are many definitions to being honorable, some are:
The Bushido code of the samurai that is said to have emphasized virtues such as loyalty, honor, obedience, duty, filial piety, and self-sacrifice.
Chivalry of medieval knights with ideals of knightly virtues, honor and courtly love, pride aspiring to beauty, and formalized pride giving rise to a conception of honor, which is states as the pole of noble life.
It should be noted that the principle idea is not being "good", but being "just" and "true to one's word" and in that sense even criminal organizations such as Yakuza consider themselves honorable.
This trait is intended to be used for characters that make it into a habit to mention that they are honorable, bound by a code of honor like Bushido or chivalry, just, fair, true-to-their-word, etc. And should not be applied to every character that looks honest.