A Mystic Code (礼装, reisō?) is a support weapon that an adult magus carries as a magical artifact. There are two general types of Mystic Codes.
The first kind functions as an amplifier. They are an orthodox Mystic Code for support, that can be used for prana amplification or storage, prepared to strengthen a spell. Tohsaka Rin's jewelry and Kokutou Azaka's salamander glove are of that kind.
The other type is a Mystic Code that have a predetermined usage. They are activated with the magus's prana and can perform a given mystery as long as it is supplied with energy. It becomes a spell in itself; many of the Noble Phantasms of Servants are usually of this type. Their usage is unique, so they aren't really generic, but this also means they can be tremendously efficient in what they do.
A regular Mystic Code wouldn't be much of a weapon against Dark Sakura, but the jeweled blade Zelretch, which is the latter type, is kind of a foul play as it can start up the Second Magic.
Source: the Tsukihime Laboratory entry.
Emiya Kiritsugu's Mystic Code is a pistol, a Thompson Contender. Kayneth Archibald El-Melloi's is the Volumen Hydragram. The Tohsaka family uses jewels, following the teaching of their master Kishua Zelretch Schweinorg.