Step 1: Identify the speaker.
Arun is the one speaking, so every relationship is measured from Arun.
Step 2: Unpack my father's only son.
Arun's father has exactly one son. Since Arun is male and is that father's son, the only son must be Arun himself.
Step 3: Replace the phrase.
So my father's only son simply means Arun.
Step 4: Rewrite the full sentence.
The woman is the daughter of my father's only son, which now reads the daughter of Arun.
Step 5: Name the relation.
A woman who is the daughter of Arun is, of course, Arun's daughter.
Step 6: State the answer.
Therefore the woman is Arun's daughter.
\[ \boxed{\text{Daughter}} \]