The phrase often refers to the malleability of human kind: The ability that we all have to transform and be transformed by the many experiences we endure throughout our life. Also, it is an allegory to the creation of man from the group by God and the making of Adam. It is also the precursor to the phrase "from dust you come, to dust you will return", as the clay packs that same ethereal dust from which man was supposedly created.
It also pays tribute to the fact that we are not the strongest, nor the toughest, nor the most perfect. We are simple creatures...made of clay. It is a call to humbleness, a remembrance of our imperfections, and a reminder that all that we may destroy, we can create again.
One way to interpret the title of the story is in light of the Biblical account of the creation of Adam:
And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul. (Genesis 2:7)
Although Allende herself rebelled against the Church, and has stated in interviews that she is not traditionally religious, she was writing in an environment which was predominantly Roman Catholic and would be familiar with Christian symbolism.
A second element of this religious allusion is the notion that "all are of the dust, and all turn to dust again," repeated in the Ash Wednesday liturgy during the imposition of ashes (Ecclesiastes 3:20).
In the story, Azucena has been buried in mud during an earthquake and is slowly and painfully dying as she returns to the earth both in the metaphorical sense (death) and literal (buried in a mudslide).
As well as destruction, though, there is creation in the way Rolf Carlé, the protagonist, reconnects with his own emotions as he attempts to console and support the dying girl.
it is ironic that we are all made of clay by god and when it is our time to die we will be covered with clay again