“Atop” is not common, at least in the US, but it generally means means “on top of and supported by (touching the top surface of, or resting on the top surface of)”. Example: There is a large sign atop the building. “Above” does not carry the same implication of resting on or touching the top surface. Example: There is an airplane flying above the building. “Atop” can also be used in non-physical ways. Example: Tiger Woods is atop the leader’s board at the tournament (meaning, he is listed in first place, ahead of all the other competitors).

1. Atop

- something on the top of another thing

examples:

It was sat atop the table.

She was atop Mount Everest

2. Above

- something is over another thing.

examples:

There were birds flying above us.

The mayor lives ten floors above me.

note: most native english speakers do not use 'atop' very often. Usually they would say, "it was on the table" or "she was on top of Mount Everest"