Hi
Deer can eat both plants and animal meat depending on its species. When a deer finds an apple, it will most probably eat the apple in whole.
As the apple contains seeds inside it, so along with apple flesh, seeds will also move through the digestive tract of the deer and come out of its body in feces. Therefore, when the deer reaches in new location while moving or grazing, the seeds will be dispersed from the feces and reach soil where they can grow into new plants.
The seed dispersal can occur through many ways like wind and water. The dispersal of seeds through animal feces is also an important mode of dispersal.
Hope it help!