dissension: a community's open split into rival factions, the point where quarreling breaks out into two camps facing off.
The word paints a picture of "standing apart": two groups taking up positions against each other. Long before the New Testament it carried a political charge, used by Greek writers for the way a city or a people could tear itself into rival factions. Paul reaches for this somewhat formal word to name a specific danger in his churches, the moment when disagreement stops being private and becomes a public split.
It helps to see where this word sits among its neighbors. It is stronger than plain quarreling (ἔρις), which is the heat and the arguing itself. It is not yet a settled, self-identified party or sect (αἵρεσις), which is what a division becomes once it hardens and organizes. And Paul tends to use a different word for a "tearing" (σχίσμα) when he names the concrete cliques at Corinth. This word marks the in-between stage: the point where the arguing has congealed into two camps facing off across the room.
In every place Paul uses it, the concern is the same. It is not honest difference of opinion, but the kind of division that breaks the unity of a community. In Galatians it stands in a list of the harm that self-centered living does, and in Romans it names the trouble stirred up by people who set believers against the teaching they had received.