The law of conservation of matter states that in a closed system, the total mass remains constant regardless of the processes occurring within it. This principle is similar to the law of conservation of energy, where energy can neither be created nor destroyed, only transformed. An example provided is a combustion reaction of ethanol in a closed flask, where the mass before and after the reaction remains unchanged. However, in an open system, this law does not hold because matter can enter or leave freely. Understanding this concept is crucial for grasping fundamental chemical reactions and their implications.