O, dinlerken not alıyor, bu yüzden daha iyi hatırlıyor.

The comma after O is stylistic; it is not grammatically required.
You can write the sentence as:

• O dinlerken not alıyor, bu yüzden daha iyi hatırlıyor.

Both versions are correct. The comma can be used in writing to give a small pause after the subject, but in everyday texts it is often omitted.

dinlerken means while (he/she/they) is listening or when (he/she/they) listens.

Formation (simplified):

• Verb: dinlemek – to listen
• Aorist (simple present) 3rd person: dinler – he/she listens
• Add the suffix -ken – while / when doing X
• dinler + ken → dinlerken – while listening

The suffix -ken does not change with vowel harmony; it stays -ken.

In dinlerken, the subject is understood to be the same as the subject of the main clause.

• Main clause subject: O … not alıyor – He/She is taking notes
• Time clause: dinlerken – while (he/she) is listening

Turkish often “shares” the subject between a main clause and clauses with -ken, so you do not repeat o inside dinlerken.

not alıyor literally is is taking note(s).

• not – note, borrowed from European languages
• almak – to take
• alıyor – is taking / takes

Turkish often uses a noun plus a light verb like almak to form a single meaning. not almak is the standard way to say to take notes.

In Turkish, the direct object is marked with -(y)ı / -(y)i / -(y)u / -(y)ü (accusative) when it is specific or definite.

• not alıyor – he takes notes (in general; non‑specific notes)
• notu alıyor – he is taking the note or he is taking that specific note

Here we are talking about note‑taking as a general habit, so not stays unmarked: not alıyor.

Both tenses can describe habits, but they feel different:

• not alıyor – often used for a current, typical, or characteristic behavior, especially in spoken Turkish: He takes notes (as something he tends to do).
• not alır – more like a general fact or rule: He takes notes (as a rule, generally speaking).

In everyday speech, -yor is very common even for repeated or typical actions, especially when you are describing a person’s characteristic way of doing things. That is why not alıyor sounds very natural here.

bu yüzden literally means for this reason or because of this and is used like so / therefore.

Similar expressions:

• bu yüzden – for this reason, so
• bu nedenle / bu sebeple – very similar, a little more formal
• o yüzden – for that reason, so

They can usually replace each other without changing the basic meaning: … not alıyor, bu yüzden / bu nedenle / o yüzden daha iyi hatırlıyor.

Turkish forms the comparative with daha placed before an adjective or adverb.

• iyi – good / well
• daha iyi – better (literally more good / more well)

So daha iyi hatırlıyor means he remembers better or he remembers more well. The word order is fixed: daha comes right before iyi.

Formally, hatırlıyor is present continuous (is remembering), but in a sentence like this it is best translated as remembers.

• daha iyi hatırlıyor – he remembers better / he has a better memory (as a result)

As with alıyor, the -yor tense is often used for general tendencies or characteristic behavior, not only for actions happening right now.

Both are possible, but there is a nuance:

• dinlerken not alıyor – He takes notes while (he is) listening.

  • Focus on simultaneity: the two actions are happening at the same time.

• dinlediğinde not alıyor – When he listens, he takes notes.

  • Focus on whenever or when he listens; sounds a bit more like a rule or repeated event linked to a time point.

In your sentence, dinlerken is slightly more natural because note‑taking clearly happens during listening.