The framework of universal composability (UC) is a general-purpose model for the analysis of cryptographic protocols.
UC guarantees very strong security properties… protocols remain secure even if arbitrarily composed with other instances of the same or other protocols. Security is defined in the sense of protocol emulation. Intuitively, a protocol is said to emulate another one, if no environment (observer) can distinguish the executions. Literally, the protocol may simulate the other protocol (without having access to the code).
The notion of security is derived by implication. Assume a protocol $P_1$ is secure per definition. If another protocol $P_2$ emulates protocol $P_1$ such that no environment tells apart the emulation from the execution of the protocol, then the emulated protocol $P_2$ is as secure as protocol $P_1$.