An idea or behavior is normative if it is normal for people promote that idea or behave in that way.
Within philosophy, Normative Ethics offers theories of the right way to behave. Although on surface normative ethics is trying to derive proper behavior from scratch, the reality is that “normative” ethical theories do not become popular when they come to conclusions that are not already generally held (socially normative). So normative ethics could be seen as an attempt to figure out the rules behind what we are already doing.
In social science, the view is that norms are put into us by our socialization, and that the nature of norms is fairly arbitrary (Moral Relativism).
Philosopher John Skorupski says a normative statement is something you believe for a reason. We think this is backwards. Moral and motivational claims are something you would never believe without a reason (some sort of story), unlike factual claims, which you might directly perceive. Supporting evidence for norms and value judgments often takes the form of factual claims, or causal claims and related counterfactuals and predictions. “We must do X, because if we don't, then Y will happen.” We might be able to investigate the truth of the causal claim, but the argument will inevitably also rely on other unspoken (normative) assumptions (that Y is bad).
Saying something is normative is the opposite of saying that we believe it for a reason (other than social conformity, and perhaps survival). Where norms clearly do come into it is that if a judgement is normative, then we can expect to make that claim without having to give a reason. When we have non-normative value judgments, we learn to keep quiet about those.
This connection between value judgments and reasons is another take on the Is vs. Ought distinction. It is more flattering to the validity of our judgments if we see them as flowing from reasons, rather than seeing them as fundamentally lacking in truth, and so needing support by explicit knowledge.
See Is vs. Ought