In physics, it is important to understand the distinction between conservative and non-conservative forces. For one thing, it comes in handy when trying to solve problems using a work/energy approach, which countless mechanics students are no doubt busily doing as I write.
The conservation of energy principle is merely a statement of the first law of thermodynamics, which, for mechanics, translates to: "The change in the total mechanical energy of a system between states 1 and 2 is equal to the total work done on the system by non-conservative forces between states 1 and 2." The term 'state' refers to a particular position and velocity of the system's components (time does elapse in between states, but the particular amount is not significant for the analysis).
In equation form, these words look like this: