to make beautiful or glorious: to adorn, to bestow honor, or, of oneself, to display or claim splendor.
This is a word about visible splendor. Its noun cousin names a beautiful headdress or turban, the finery worn on a festive day, so the verb keeps that flavor: to make something or someone shine, to dress them in glory. When people are the ones acting, they beautify a place, most often God's temple, decking it out so that it looks as glorious as what it houses.
When God is the one acting, the same word turns from decoration to honor: he glorifies his people, giving them a beauty and standing they could never win for themselves. Isaiah returns to this again and again, promising a battered nation that God will adorn them like a bride and be glorified in them.
The reflexive side, where the action turns back on the doer, cuts two ways. When God displays his own splendor through Israel, it is right and fitting. When a creature does the same against the one it owes everything to, it becomes an ugly boast: Gideon's army is trimmed so Israel cannot vaunt itself over God, and a proud empire is mocked as an axe that struts against the hand swinging it. The line between glory and arrogance is simply who has the right to the splendor being shown.
See also the neighboring words for honor and praise: the word for weightiness and importance (כבד), which grounds glory in gravity rather than beauty, and the ordinary word for praise (הלל), whose reflexive is the everyday word for boasting.