The speaker in this poem does not seem to be engaged in many specific activities so much as reflecting deeply on his work in harvesting the apples. The speaker also seems to be drifting in and out of sleep and dreaming, which imbues this poem with a richly symbolic (one might argue allegorical) meaning, touching on the themes of hard work, success and satisfaction, or perhaps life and death.
"The great harvest" that was once valued by the speaker in this poem could be said to be the wealth, recognition and achievements that the speaker has laboured hard to gain throughout his life. It is interesting therefore, that the speaker says he is "overtired" of this great harvest that he once wanted. Perhaps this reflects that the speaker has too much of what he wanted and now feels neither joy nor satisfaction, but exhaustion, from his achievements. This can be seen to be symbolic of how mankind works very hard to get something, yet often when we finally have achieved our objective, we are not able to rest and relax - the act of possession robs the objective of its value, and we are left restless once more. It is interesting that the word "sleep" occurs often in the poem and there are lots of references to dreaming. This could be symbolic of the death that awaits the reader. Apple harvest is in autumn, and perhaps the speaker has reached the "autumn years" of his life and is now reflecting on his achievements over his lifetime, and awaiting death.
Other examples of symbolism which might fit into this reading of the poem are contained in this passage:
My long two-pointed ladder's sticking through a tree
Toward heaven still,
And there's a barrel that I didn't fill
Beside it, and there may be two or three
Apples I didn't pick upon some bough.
But I am done with apple-picking now.
The ladder pointing heavenward might symbolise thoughts of the afterlife or spiritual longins, and the unfilled barrel and apples might represent the unfinished tasks of life. It is clear, however, that the speaker is not going to carry on with his job - he is weary of the tasks of life.