Air resistance is basically like frictional force. When tension force equals the frictional force, net force is zero and thus the velocity will be constant after that (a = 0). Similarly, when force of air resistance (air "Friction") balances the force of gravity, the velocity of the falling object will be constant (a = 0). This final constant velocity is basically the terminal velocity they are talking about. And then I just understand the relationship that terminal velocity is high for objects of greater masses because heavier objects have greater force of gravity (F = mg) and thus air resistance has to apply more force (put more "effort" if you will) if it wants to cancel the F due to gravity. And to consolidate this surmounting force, air friction will need some time...and as it takes its time, the velocity keeps on increasing...and by the time air friction finally manages to cancel force due to gravity, the object has already reached a very high velocity (terminal velocity). This is also why heavier objects reach the ground faster than lighter objects in the presence of air resistance.
In other words, just like life, air resistance needs more time to tackle a more formidable "enemy".