Secrecy was the action of keeping something hidden or the state of something being kept hidden. The hidden something was known as a secret.
In 2254, the medical state of the survivors from the crashed SS Columbia was described by Doctor Phil Boyce as being excellent. Doctor Theodore Haskins said there was a reason for their condition, but he was not sure if Earth was ready to learn this information. He gave permission for Vina to show Captain Christopher Pike the secret to their excellent health. (TOS: "The Cage")
In 2268, after the theft of a Romulan cloaking device by the USS Enterprise, a female Romulan commander supposed that very soon the Romulans would learn to penetrate the cloaking device. According to Lieutenant Commander Spock who agreed with the assessment, military secrets were the most fleeting of all, though he had hoped that they had exchanged something more permanent from their time together, which the Romulan commander stated would be their secret. (TOS: "The Enterprise Incident")
That same year, Tribal Priestess Miramanee on the planet Amerind told an amnesiac Captain James T. Kirk about the Wise Ones who chose a medicine chief to keep the secret of "the Temple" and to use it when the sky darkened. Kirk correctly assumed that the secrets were passed from father to son, but pondered why Salish the previous medicine chief didn't use it. His father died before he could share the secret. (TOS: "The Paradise Syndrome")
In 2373, The Doctor referred to holograms inside a holodeck version of the Paxau Resort as automatons and mannequin simulacra with no secrets to reveal. (VOY: "Darkling")
Starfleet Command classified all knowledge of Omega molecules as a military secret of the highest order and enacted the Omega Directive, on which only starship captains and flag officers were briefed. (VOY: "The Omega Directive")