The word *filiae* can be either genitive or dative; the two cases look alike in the singular of the first declension.
If you read it as a genitive, then *filiae* is indeed "of the daughter" and this translation is correct:

> *Agricola filiae aquam dat.*  
> The farmer of the daughter gives water.

If you read it as a dative, then *filiae* means "to the girl", leading to a different translation:

> *Agricola filiae aquam dat.*  
> The farmer gives water to the daughter.

They are both equally correct readings of the Latin sentence.
Only context determines which is correct.
The second one makes more sense here; "farmer of the daughter" sounds unusual.

In your book the intended translation is the second one I give.
But it does not specify the relation of the farmer and the daughter at all.
You can add a "his", but Latin behaves very differently to English here.
The word *suus* is an adjective modifying the daughter, not a genitive of the farmer.
It has to have the same number, gender and case than the daughter.

Thus the most natural translation would be:

> The farmer gives his daughter water.  
> *Agricola filiae suae aquam dat.*