Learn Hardcore Latin: Serva aviae acum tradit, ut tunicam laceram consuat. - The maid hands the needle to grandmother, so that she may sew the torn tunic.

Because aviae is in the dative singular. The dative case often marks the indirect object, especially with verbs of giving, showing, telling, and handing over.

Here, tradit means hands over / gives, so Latin uses:

serva = the slave woman (subject)
acum = the needle (direct object)
aviae = to the grandmother (indirect object)

So aviae answers the question to whom?

Why is serva the subject?

Serva is in the nominative singular, which is the case normally used for the subject of the sentence.

So in Serva aviae acum tradit, the person doing the action is serva:

serva = the slave woman
tradit = hands over

Even though English depends heavily on word order, Latin usually shows the subject by case ending, not just by position.

Why is acum in the accusative?

Because acum is the direct object of tradit.

The verb trado means hand over, give, deliver, and the thing being handed over is the direct object. In this sentence, that thing is the needle: