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In thermodynamics, a system is the continuous area of space that we are interested in. This is contrasted against the surrounding, or environment, which is the rest of the universe.
A system has the potential to exchange heat, volume, and particles with the surroundings. A system which does not exchange heat is called adiabatic. A true adiabatic system does not exist, but systems can become very close to this approximation.
Systems that exchange volume are actually very common; they are usually called pistons. In a piston, one side is able to move up and down, and this allows us to extract or input work to the system. A system that does not exchange volume is called isochoric.
A system that is able to exchange particles with the surrounding is called open. These aren't used very much, and we will mostly be considering it's counterpart: closed systems. A system is closed if it is unable to exchange particles.
If a system is both closed and adiabatic, then it is called isolated. Again, these systems do not actually exist, but are merely idealizations.
System: The part of space we are interested in. Surroundings: The part of the universe that is not the system. Adiabatic: A system that cannot exchange heat. Isochoric: A system that cannot exchange volume. Open: A system that can exchange particles. Closed: A system that cannot exchange particles. Isolated: A system that is both closed and adiabatic.