What exactly is a Blackguard's vice? What's the meaning of it? Is it some kind of unholy symbol or just a kind of feeling? Blackguard is from Heroes of Shadow 4e.
The answer is partly explaining English vocabulary, and partly explaining how D&D 4e has used that English vocabulary to mean something game-specific.
In English, vice means
moral depravity or corruption, wickedness; a moral fault or failing
Vices are behaviours and personality features that make someone spiritually and morally bad, in the same way that virtues are behaviours and personality features that make someone spiritually and morally good.
This is an old meaning of the word and an old way of thinking about people and good and evil — there are other related meanings that don't have the same exact meanings, but fantasy RPGs almost always use old meanings of words when there are multiple. That's the case here with vice.
How the game is using the term vice is to contrast with a paladin's vows, which are expressions of a paladin's virtuousness. Instead of taking a moral vow like a paladin, a blackguard indulges in an immoral desire or behaviour: domination or fury are the two options statted up in Heroes of Shadow.
So it is sort of a feeling, but not exactly. It is definitely not a physical symbol. It is a personal moral flaw that the blackguard encourages in themselves, to make it their personal expression of their evil.