A code is a system to convert a piece of information into another form. Codes were most often used to send messages or define situations.
Codes were often used to encrypt information, including the Federation's Code 2 and Code 3 in the 23rd century, the former had been broken by the Romulans by stardate 3478.2, and thus was replaced by the latter. (TOS: "The Deadly Years")
Many other codes were simply used to transmit information quickly, including Code One alert to indicate a declaration of war or disaster (TOS: "Errand of Mercy"), code 7-10 to indicate planetary quarantine (TOS: "A Taste of Armageddon"), Code 1-Alpha-Zero for a ship in distress (TNG: "Relics"), Code Factor 1 for a possible invasion of the Federation (TOS: "The Alternative Factor"), code blue, or blue alert, which used to indicate a change in starship flight status (TNG: "Brothers"), code white resuscitation to indicate the need to resuscitate a dead individual (VOY: "Initiations"), Emergency Code 1 for intruder alert (TNG: "The High Ground"), and Transporter Code 14 to destroy an object in a transporter beam. (TNG: "Captain's Holiday")
Critical ship systems required passphrase access in the form of prefix codes (Star Trek II: The Wrath of Khan; TNG: "The Wounded") and authorization codes. (Star Trek: First Contact; VOY: "Deadlock", "Dreadnought", "Cathexis", "Renaissance Man"; TNG: "Chain of Command, Part I")