Invariant of Motion: Understand in Plain English

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The invariant of motion refers to a principle in certain systems where the total mechanical energy, defined as the sum of kinetic and potential energy, remains constant. This means that in a conservative system, energy is neither created nor destroyed but transformed between kinetic and potential forms. Understanding this concept is crucial for analyzing dynamic systems in physics. The discussion emphasizes the importance of mechanical energy conservation in explaining system behavior. Overall, the invariant of motion highlights a foundational principle in energy dynamics.
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Can anyone please describe me the following theory in plain english. Your help will be much appreciated.

"In certain types of systems there is an invariant of motion which is equal to the sum of the kinetic energy and the potential energy of all the particles in the system. This quantity is the mechanical energy of a dynamic system, and in a conservation system it remains constant."
 
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It's saying that in some systems mechanical energy is conserved.
 

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