I'm a beginner in Esperanto, and I am learning it on Duolingo. I came across a sentence that referred to a single apple as "pomon" instead of "pomo." I thought that nouns always end in "o." When would you add an "n" onto them.

I eat apples - I eat THEM, not THEY. So 'Mi manĝas pomojN' not 'pomoj'.
In singular in modern English there is only 'it', so you can check only by plural.

To elaborate what Sergejm said...

Both adjectives (ending -a) and substantives (ending -o) undergo inflection for number and grammatical case. For number this simply means, that they take an ending (-j) showing that they are more than one, i.e. plural, unu pomo, multaj pomoj.

E-o has two grammatical cases: nominative (no special ending) and accusative (ending -n and it comes after the possible plural marker). You use accusative to distinguish the direct object of the action of the verb (Mi manĝas pomojn.), cf. English which uses only word order for that(*). For a quick intro see the video by Paul on Langfocus channel in Youtube.

*: Relying solely on word order causes a couple of things: the word order must be strict and you need formal subjects (What is that "it" in "It rains"?). For speakers of languages with a more free word order and no formal subjects these cause sometimes difficulties.