The staged combustion cycle is a thermodynamic cycle of bipropellant rocket rocket engines. Some of the propellant is burned in a pre-burner and the resulting hot gas is used to power the engine's turbines and pumps. The exhausted gas is then injected into the main combustion chamber, along with the rest of the propellant, and combustion is completed.
The advantage of the staged combustion cycle is that all of the engine cycles' gases and heat go through the combustion chamber, and overall efficiency essentially suffers no pumping losses at all. Thus this combustion cycle is often called 'closed cycle' since the cycle is closed as all propellant products go through the chamber; as opposed to open cycle which dumps the turbopump driving gases, representing a few percent of loss.
Another very significant advantage that staged combustion gives is an abundance of power which permits very high chamber pressures. Very high chamber pressures mean high expansion ratio nozzles can be used, whilst still giving ambient pressures at takeoff. These nozzles give far better efficiencies at low altitude.
The disadvantages of this cycle are harsh turbine conditions, more exotic plumbing is required to carry the hot gases, and a very complicated feedback and control design is necessary.
Staged combustion engines are the most difficult types of rocket engines to design. A simplified version is called the Gas-generator cycle.