This is an inter-related set of proof points to prove a hypothesis. It’s a little hard to grasp, but it basically means “a mountain of related evidence.”
From Oxford Reference:
A lawful pattern of interrelationships that exists between hypothetical constructs and observable attributes and that guides a researcher in establishing the construct validity of a psychological test or measure.
Two researchers coined the term in 1955, based on the Greek word for law. They stated that a nomological network of evidence for a point should generate testable hypotheses.
“Nomology” is the study of scientific laws. So a nomological network is a group of laws for an argument.