According to the dictionary,
to take hold of something and pull it several times
Mary was pulling nervously at her hair.
For example, a fisherman pulled at/on his fishing rod.
Now say, you are standing in front of a door but can not open it because it is blocked by some very heavy thing on the other side.
It is very hard to push the door and the heavy thing all in one go.
Instead, most people will push the door repeatedly several times with the hope that will make the crack or gap bigger so that we can squeeze through the the crack or gap.
Do we say "push at/on something" to mean "to take hold of something and push it several times", the same way we say "pull at/on something"?