Screengrab of interactive multimedia clip from Physical Chemistry textbook (click to enlarge)

In order to understand the workings of a physical process or chemical reaction, a limited area of study must be isolated.  This area is usually described as the system and can be as large or as small as necessary.
Any area not included in the system is considered the surroundings.  Thermodynamics is the study of heat and other forms of energy in both chemical and physical processes in specific systems.
The first law of thermodynamics follows the law of conservation for heat.  Simply stated, heat can not be created or destroyed, merely changed from one form to another.  The second law involves the amount of order involved with a spontaneous reaction in a system.
In order to understand, and thereby utilize, these two laws, two main thermodynamic units must be defined.  The first is enthalpy, H, which describes the amount of heat involved and the second is entropy, S, which describes the amount of order or disorder in a system.
Using these two units and the temperature inside a system, the amount of free energy, G, or energy available to do work can be determined using the Gibbs equation, G = H – TS.  Ultimately, the spontaneity of a system can be determined.
The three states of matter, solid, liquid and gas and their phase transitions, melting, freezing, vaporization, condensation and sublimation are intertwined with discussions of spontaneity.  Equilibrium between these states and inside both chemical and physical processes is of equal importance.
While equilibrium can be discussed in many forms, the thermodynamic discussion of a system at equilibrium related to the free energy is the most useful in thermodynamics.  As a system that is at equilibrium has no free energy, the forward and reverse directions are equal, and the following equation can be derived

∆G = -RTlnK where K is the equilibrium constant of a reaction.

Through this equation, and others similar to it, the free energy and spontaneity of a system can be determined through changes of temperature and concentrations of individual components.
In section 1.3, (download Physical Chemistry free Chapter 1) titled Systems, States and Equilibrium, the opening paragraph introduces the concept of a system and the three types.  The accompanying figures clearly help visualize the overall definitions.

Physical Chemistry – Systems, States, and Equilibrium (click to enlarge)

I believe some common examples of each would also be beneficial.  For example, an open system could be described as an open container of hot water, either a pot of water or a glass of water.  The transfer of heat is completely familiar and the transfer of matter/material can be visibly seen as steam.
Staying with the same theme, a sealed or covered pot (or glass) would still transfer heat, but halts the transfer of steam (matter) to the surroundings.  Finally, a closed system would be an insulated, sealed cup (Styrofoam) which is a very familiar example of stopping the transfer of both heat and steam to the surroundings.