Today, we will be discussing: What is meant by “Full-flow staged combustion cycle” — the one that mighty Raptor Engine has got. The idea of this article is to give you a complete layman’s explanation.
One Tip: Try not to get bogged down by the flow diagrams of the engine. Focus more on the text content.

First: Staged Combustion (Closed Cycle)
You have got two propellants: Fuel & Oxygen, in their independent cylinders. They both have to meet in a combustion chamber to ignite and produce a massive amount of thrust. So we connect high-pressure pumps which pump the propellants out to meet down the line in the combustion chamber. Now the pumps also need the energy to run. So, we bring an intermediate “stage”. The pumps, pump the propellant to a pre-burner — a mini-engine. Here a mini-combustion happens which then runs a turbine and this turbine powers the pumps and makes everything above go in a cycle.

Let’s build on this further.
In the combustion chamber, the ratio of propellants is kept optimum. To utilize the right amount of oxygen to burn the complete fuel. This optimization if done in the mini-engine will lead to a very high temperature, which would pose a difficulty for the turbine and mini-engine. So what we do is, force a non-optimum propellant ratio to go through the pre-burner. Send all of the one propellant and a tiny amount of other. So the pre-burner is either Fuel rich or Oxygen-rich.
After the pre-burner runs the turbine, the entire exhaust is forced to go through the combustion chamber, so that whatever “extra” propellant it was having, undergoes combustion. This is called Propellant-rich staged combustion. The propellant can be fuel/oxygen.
Let’s build further.
Until now we are having one preburner (mini-engine) pumping both propellants. In some cases, the amount of fuel & propellant needed to be pumped can be quite similar and for some, it can be very different. For the latter case, each will need its own pre-burner. So, now there can be two engine types. One has the same propellant-rich pre-burner for both the pumps or has a fuel-rich pre-burner for the fuel pump and oxygen-rich pre-burner for the oxygen pump. The first case is called “Propellant-rich dual shaft/burner staged combustion” and the second case is called “Full flow staged combustion”.

I hope the above was clear. Feel free to ask questions.