Surroundings
The system is the part of the universe we wish to focus our attention on. In the world of chemistry, the system is the chemical reaction. In thermodynamics we follow energy flowing from one place to another during chemical or physical changes. To be able to quantify these changes rigorously, it is important for us to define what specifically is changing. To accomplish this we pick a specific part of the world that we are interested in and we call it "the system".
For a given change (process), the system is what we are interested in. It is the matter and the total energy associated with that matter. For example, if we wanted to understand the energy change of ice melting in a glass at room temperature. Let's imagine that for this process the ice is initially at temperature of 0°C and then melts and the ending liquid water is 25°C.
2H2 + O2 ---> 2H2O
The surroundings are everything else; the rest of the universe. For example, say the above reaction is happening in gas phase; then the walls of the container are part of the surroundings. In the ChemTeam classroom, I say to my students "You are the system (that is, the chemical reaction) and as you look outward, everything else are the surroundings.
There are two important issues:
1. A great majority of our studies will focus on the change in the amount of energy, not the absolute amount of energy in the system or the surroundings.
2. Regarding the direction of energy flow, we have a sign convention.