El ejemplo que puso la profesora me aclaró una diferencia que antes no veía.

It is a relative pronoun meaning that or which. It links el ejemplo to the clause puso la profesora.

So:

el ejemplo = the example
que puso la profesora = that the teacher gave

Inside that clause, que stands for el ejemplo.

Spanish word order is more flexible than English word order. Que puso la profesora is a very natural structure in Spanish. It still means that the teacher gave.

You could also say el ejemplo que la profesora puso, but the version with puso la profesora often sounds smoother and more natural in this kind of sentence.

Aclarar means to clarify, to make clear, or to clear up. In this sentence, me aclaró means it made clear to me or it cleared up for me.

The me is an indirect object pronoun. It shows who received the clarification: me = to me / for me.

Aclaró is the preterite, so it presents the action as a completed event. The idea is that the example had a clear result at a particular moment: it clarified something for the speaker.

If you used aclaraba, it would sound more ongoing, habitual, or descriptive, which is not the main idea here.

Veía is the imperfect, which is often used for background situations, ongoing states, or things that were generally true in the past.

Here, antes no veía means something like before that, I wasn't seeing/noticing it or I couldn't see it before. It describes the speaker's earlier state of understanding, not one single moment.

The second que refers to una diferencia.

So:

una diferencia que antes no veía = a difference that I hadn't seen/noticed before

It does not refer to el ejemplo.

Not necessarily. In Spanish, ver is often used in a more abstract way too. Here it means something like to notice, to perceive, or to recognise.

So no veía una diferencia is closer to I wasn't noticing a difference or I couldn't see a difference than to literal eyesight.

Yes, but the meaning would change slightly. Me makes the sentence personal: the example clarified the difference for me.

Without me, the sentence would sound more general, as if the example simply clarified the difference in itself. In this context, me is very natural because the speaker is talking about their own understanding.

The accent mark shows that aclaró is the third-person singular preterite: he/she/it clarified.

Compare:

aclaró = he/she/it clarified
aclaro = I clarify

So the accent changes both pronunciation and meaning.