Learn Russian: Люди часто прикрывают глаза от яркого солнца. - People often half-close their eyes from the bright sun.

The prefix при- adds an "attenuative" meaning, showing that an action is done slightly or incompletely. While закрывают would mean people completely shut their eyes, прикрывают means they only partially close or shield them.

Why do we use the preposition от instead of из-за for "from the bright sun"?

In Russian, от (followed by the genitive case) is used to express a direct, often involuntary physical or emotional reaction to an external stimulus (like squinting from bright light or shivering from cold). Из-за is used for logical reasons, indirect causes, or obstacles.

Does прикрывают глаза mean they are squinting, or actually putting their hands over their eyes?

It can mean both! The root verb крыть means "to cover". Combined with the incomplete-action prefix при-, прикрывать глаза can refer to partially closing the eyelids (squinting) or partially covering the eyes with a hand to shield them.

What is the perfective equivalent of прикрывают if we wanted to say "he half-closed his eyes" just once?

The perfective form is прикрыть. If you were talking about a single, completed action, you would say он прикрыл глаза. In our sentence, we use the imperfective present-tense прикрывают because the word часто (often) tells us this is a repeated, habitual action.