to go well, be pleasing: for something to turn out good or to seem good to someone
In its plain form this verb describes a situation or a thing as turning out well, or as striking someone as good. It is the everyday way of saying that life goes well for a person, that a plan succeeds, or that a proposal pleases the one who hears it.
A very common pattern is impersonal: "it went well with so-and-so," meaning their circumstances prospered, often as a reward for obedience. This is the language behind the promise attached to honoring one's parents, that it may go well with you and your days be long. The same form, with the phrase "in the eyes of," says that a word or a deed looked good to someone, that they approved of it. The two shadings, prospering and pleasing, are the same idea seen from two angles: the thing is good, whether good in its outcome or good in someone's judgment.