To answer this question you need to think about the context of this poem. We are not given any firm details, but we can infer that the speaker has just found out for some reason that the love she has for a man is not returned. Thus this poem captures the age long agony of unrequited love, or of love that is expressed towards someone else but not returned. Trying to move on from this experience and put the emotions, feelings, thoughts and memories behind you is incredibly difficult. Thus it is that the speaker expresses her desperate desire in the first line of the poem:
Heart! We will forget him!
Her earnest wish is to somehow forget the man she was in love with and move on. However, as we read the poem, we begin to understand that despite this desire, she will find it far more difficult than she thinks, and "moving on" is not that simple.