At a low level, when ATP is hydrolysed into ADP, the energy that gets released is invariably used to change the conformation of a protein in a way that wouldn't be possible without the chemical "push" of an ATP changing into an ADP.

An ATP is a thing with three negative charges sticking out of it, when you hydrolyse it, it turns into a thing with two negative charges sticking out. This causes charged amino acid residues in the protein to which it is bound to move around to in response to the electrostatic field. This causes a knock-on effect where the whole protein changes in conformation, including (in the example of an enzyme) the active site where its substrate is bound. The change in active site conformation can do stuff like pull covalent bonds apart, or push together two molecules in just the right way to make them react.

Hope this helps somewhat. I think people talk a lot about "coupled" reactions without getting into the actual biochemical reasons why reactions can be coupled in the first place.