The chair is the favorite spot of the twins' master, who keeps them as slaves.  They fan the chair to keep it cool, even in his absence.  The action represents just how ridiculously oppressiono of slavery, and the thwarting of a person's own lives and dreams in favor of the lives and dreams of someoneelse. 

Here is a passage from the novel that illustrates the argument:

(…) Hmm… woe the childless woman, they warn. Let someone go and see their mother, who is she? Where is she sitting? While they stand here fanning an empty chair? Let someone go and see how she suffered bearing them. The nine months of dizziness, when food tasted like dung and water like urine. Nine months of unwholesome desires and evil dreams. An then the hour of the breaking of the amnion, where the space between her life and her death wore thin like a needy woman’s hair thread. (…) Did she go through all that and with her rest at the end postponed so they will come