System
Definition
The part of the universe you are studying: the reaction flask, the beaker, whatever you have chosen to focus on. Everything else is the surroundings.
Technical definition
In thermodynamics, the system is the defined portion of matter or region of space under study, classified as open (exchanges matter and energy), closed (exchanges energy only), or isolated (exchanges neither). All thermodynamic quantities are defined relative to the system.
Example
In a calorimetry experiment, the reacting solution is the system and the calorimeter plus the lab air are the surroundings.
Common confusion
System and surroundings are choices, not fixed things. You define the boundary, and energy crossing it is what you track: moving the boundary changes the analysis.