If we think about this poem as a poem about the speaker's attitudes at the end of his life, I think we can see what the barrel signifies. I believe that it signifies the things in life that the speaker would have liked to do but was unable to do.
Scholars argue that the apple harvest is a metaphor for the speaker's life. He has finished with all the work he is going to do, he is tired and ready to die. But there is still this barrel he didn't fill as well as those apples he didn't pick. In other words, he still has some regrets -- some things he wishes he could have done or feels like he should have done.