Az can be translated as "that", right? So "Az alma" is not "That apple"? Why is that wrong?
Because "that" is a demonstrative pronoun.
Turning back to ez and az, i.e. the demonstrative pronouns, there are two things to keep in mind. By Hungarian logic they make their object definite, therefore you need to add a definite article right after them. Examples:
ez a ház - this house
az az asztal - that table
ez a férfi - this man
az a nő - that woman
ez a Péter - this Péter (e.g. if there are more Péters in a group we’re talking about), or ‘this Péter guy’
az a szép lány - that pretty girl
ez a gyors kocsi - this fast car
The second important rule is that they are in the same case and number as the nominal they are referring to. The previous list in plural:
ezek a házak, azok az asztalok, ezek a férfiak, azok a nők, ezek a Péterek, azok a szép lányok, ezek a gyors kocsik
wouldn't alma have both short wowels? in the audio first a sounds long, like á