An enzyme is nothing more or less than a molecule or substance that makes a reaction more likely to happen.
An analogy to a boulder on a hillside is useful. The boulder could roll to the bottom (the reaction is favorable) but something must be presenting this--such a a smaller rock preventing it from moving. If an individual removes the smaller rock, the boulder rolls. Is the same way, an enzyme doesn't chance the overall reaction or the energy released (the boulder rolls just as fast if it shakes loose during a storm or you poke the restraint rock away with a stick).
To understand an enzyme, then you need to understand why a given chemical reaction is not already done, or is slow. For ATP, it is energetically favorable for the negatively charged phosphates to "get away" from each other... but they are held together by covalent bonds, and for these to be broken requires an "attack" by a water molecule that is difficult (rare). Further, the intermediate state some of the oxygens in the molecule must move through are energetically unfavorable. Any molecule that makes ANY of these things easier or more likely is an enzyme; the more of them it does, and the greater the degree it does them makes for a "better" enzyme.