Learn Hardcore Latin: Mater olivas in foro emit. - Mother buys olives in the forum.

Because mater is the subject of the sentence (“mother” is doing the buying). Subjects are usually in the nominative case, and mater is the nominative singular form.

What case is olivas, and why?

Olivas is accusative plural, because it is the direct object: it answers “what did she buy?” → olives.
It comes from oliva, olivae (1st declension feminine). The accusative plural ending for 1st declension is -ās, so oliva → olivās.

Why is it olivas (plural) and not olivam (singular)?

The Latin form tells you the number: olivas is explicitly plural (“olives”), while olivam would mean “an olive / one olive” (accusative singular). Latin often uses the plural for things typically bought in quantities.

What is in foro doing grammatically?

in foro expresses location: “in the forum / at the marketplace.”
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