A nomological network is the web of relationships a psychological construct should have with other constructs and observable outcomes if it's real and well-measured.
The term comes from the Greek nomos, meaning law, and the idea is that a genuine trait doesn't exist in isolation — it should connect to other things in predictable, lawlike ways. Take Conscientiousness. If it's a real construct, it should correlate with things like punctuality and higher grades, and it should not correlate strongly with, say, shoe size. The pattern of what it does and doesn't relate to is the network, and that whole pattern is the evidence for the construct's validity.
This idea, introduced by psychologists Lee Cronbach and Paul Meehl in 1955, was a response to a real problem: you can't directly observe a trait like Conscientiousness the way you can observe height. You can only infer it exists by checking whether it behaves the way theory says it should across many related measures. No single correlation proves anything on its own — it's the overall pattern across the network that builds a case.
This is why validating a new psychological measure takes years of accumulating evidence, not one clean study.