Learn Hardcore Russian: Я надеваю очки, чтобы лучше читать.

Наде́вать means “to put on” (an item of clothing or accessory). You use it when the action is placing something onto your body (e.g. надеваю пальто, надеваю очки).
Одева́ть also means “to dress,” but its direct object is usually a person (одевать ребёнка – to dress a child).
Носить means “to wear” in the sense of carrying or having something on habitually, not the act of putting it on (e.g. я ношу очки – “I wear glasses” regularly).

What’s the difference between the imperfective надеваю and the perfective надену?

Russian verbs come in aspect pairs:
• Imperfective (надеваю) focuses on the process or a habitual action (“I am putting on” or “I put on (from time to time)”).
• Perfective (надену) focuses on completion (“I will put on” or “I put on (and now it’s done)”).
In this sentence Я надеваю очки describes the action itself (I’m in the process of putting them on or I do this habitually).

Why does очки look the same in the accusative as in the nominative?

Очки is a plural, inanimate noun. In Russian the accusative plural of inanimate nouns matches the nominative plural form. So even though очки is the direct object here, it stays очки.

What role does play in this sentence? How is it different from or ?