to show favor: to stoop and treat someone with undeserved kindness
This is the verb behind the great Hebrew picture of grace. Its core is a free, unearned kindness shown by someone who has the power to withhold it: a king to a subject, a master to a servant, the strong to the weak, and above all God to people who cannot claim it. It is not payment for good behavior and not pity that merely feels sorry; it is a deliberate turning toward someone in goodwill.
The same act can be looked at from several angles, and they are the senses below. From above, a superior bends down and grants favor ("be gracious to me"). Aimed at the poor, that favor becomes open-handed generosity, so the word can simply mean to be kind and giving to those in need. Turned the other direction, the person in need cries out for that favor, and the verb means to beg, to plead for grace.
Because the kindness is always undeserved, the word keeps grace and need tied together. The one who gives it lowers himself; the one who asks for it admits he has no claim. This is why the Psalms reach for it so often: it is the language of a person with empty hands asking God to act out of sheer goodness.