There are two possible reasons why domestic cats push things off shelves, tables or over edges of any kind.
Domestic cats “animate” an inanimate object by pushing it over the edge of a table or shelf. The object falls to the floor and when it hits the floor it bounces around and then comes to rest. The object has moved. It is been animated and in doing so the cat has for a brief period of time created a prey object. When cats play they are, in effect, chasing prey. So this is a desire to play, to entertain himself. Perhaps he’s bored. Boredom will probably be the main reason why domestic cats push objects off shelves and tables.
An interesting aspect of this is that the domestic cat understands gravity which seems extraordinary. He knows that when he pushes an object over the edge of a shelf it will fall to the floor. How does he know that? Obviously the cat doesn’t understand Newton’s law of universal gravitation but he does understand that the object will fall. I think that that is an interesting thought.
Domestic cats are great learners. They are adaptable and adapt to the human environment. They learn how to communicate with us, to demand food and to ask to be let out of the house and let back in again for instance. They also learn how to get our attention by doing things which might irritate us. They know the things that irritate us because by accident in the first instance they have done something and seen our reaction. Therefore they do it again and get our attention.
Perhaps these two reasons should be merged together. Initially, the cat pushes an object off a shelf as a means to alleviate boredom and create something to play with. Consequently, she observes that her ‘owner’ becomes irritated, then interacts with her and talks to her. Not only has she animated an inanimate object she has also animated a lazy human who was comfortably sitting down in her armchair reading a newspaper. Fluffy liked it and wants to do it again. It worked.
Both reasons are also interlinked in that the greater the amount of interaction the human instigates with their cat, the less likely he is to knock things off shelves because he has got the attention of his human companion and has got play both at the same time.
P.S. this behavior is also linked to exploring objects. If they push over the edge they see what happens. It is part of their inquisitive nature.