The classical inquiry
Honor in the classical sense — the Greek timē, the Roman dignitas and honestas — is the social economy of recognition. What standing one has in the eyes of the community, what claims one has on its respect, how those claims are earned and lost, and what they obligate one to do. Homer is the substrate. The Athenian and Roman political cultures take it up as a structural fact of their public life.
The Roman case
The Roman version is institutionally precise. The cursus honorum is the formal sequence of magistracies an aspiring statesman climbs; dignitas is the standing one accumulates through it. Caesar's claim that his enemies threatened his dignitas is one of the load-bearing statements of the late Republic, because in the Roman political vocabulary it is not a private feeling but a public claim with real weight. Sallust, Cicero and the later imperial writers all treat honour as inseparable from the political order.
Why it matters for Virtue & Power
The platform's earlier theme on ambition already reads philotimia. Honor is the wider concept that holds ambition, duty and civic virtue together. Read closely, the late-Republic crisis is in serious part a crisis of honour — of what Roman political men understood themselves to owe each other and to the city, and of what the city would not, in the end, hold them to. See the entries on Pompey, Caesar and Cato.