We must first assume that the author intends herself to be the narrator and for the poem itself to be autobiographical. This is often not the case in any form of literature: the author is usually not the narrator.
The poem speaks of a simple childhood, perhaps lived in quasi-poverty, as well as a grandmother whose only company now is the grandchild, innocent of life's miseries. The grandmother reads jokes to the child in an effort to lighten her mood. The date is 23 September--the autumn equinox--and is probably the anniversary of someone's death (her husband's, a child's, perhaps the child's parents, as she seems to be living with the grandmother). The child in the poem is, like most children are, oblivious to the pain the grandmother is in. She is living in a world of wonder, in which the "teakettle's small hard tears / dance like mad on the hot black stove, / the way the rain must dance on the house." Then she turns her attention to drawing a childish picture of a pretty house with a man and a garden. The atmosphere, if it is autobiographical--is one of happy memories mixed with the sadness of loss.