What motivates or pushes it to dissociate more?
Perhaps surprisingly, if you could look at an individual acid molecule, it does not (or hardly) changes its behavior upon dilution. It just dissociates with a certain rate, yielding the conjugate base and a hydrogen ion. There is no "extra motivation" to dissociate, and no "tapping on the shoulder" pushing it to react.
Why is the degree of dissociation/ionisation affected by dilution?
The reverse reaction, where a dissociated acid (the conjugated base) reacts with a hydrogen ion to make the acid again, is affected by dilution. Here, two molecules have to come together, and this takes longer when the solution is more dilute.
This description is for the simplest case, where the net reaction not only describes the stoichiometry but also the mechanism of the reaction. However, even if there are intermediates, at equilibrium the forward and reverse rates are equal, and when you dilute solution, rates of the reverse steps would be significantly lowered, leading to a higher degree of dissociation.