Learn Russian: Она прищурилась, чтобы лучше увидеть картину. - She squinted a little to see the picture better.

It adds the attenuative (смягчительный) meaning, which is the focus of this lesson. While the base verb щуриться means to squint, adding при- means to do it slightly or just a little bit. This prefix often shows that an action is incomplete or done to a small degree.

Why do we use the reflexive suffix -сь on прищурилась?

Without the reflexive ending, the verb прищурить requires a direct object, such as in the phrase прищурить глаза (to narrow one's eyes). Adding -сь makes the verb intransitive, allowing you to just say she squinted without explicitly mentioning her eyes.

Why is увидеть in the infinitive form after чтобы?

Because the subject of both parts of the sentence is the exact same person (Она). When the person doing the main action is the same one performing the action in the чтобы (in order to) clause, Russian requires the infinitive. If the subjects were different, you would have to use чтобы followed by the past tense.

Could we use the imperfective видеть instead of the perfective увидеть here?

It would sound unnatural in this context. She is squinting to achieve a specific, immediate result: successfully making out the details of the picture. After чтобы, using the perfective увидеть focuses on achieving that successful result, whereas видеть would merely describe the general process or ability of seeing.