She showed me a photo of her mother from her school days.

Literal

She [topic-は] school-days [attributive-の] mother [possessive-の] photo [object-を] me [recipient-に] show-gave.

Three pieces work together. First, the noun-modifying chain stacks の particles to attach 'school days' as a setting onto 'her mother': 学校時代のお母さんの写真 ('school-days mother's photo' = 'a photo of her mother from her school days'). The の is doing extreme heavy lifting in Japanese — it's the connective tissue of compound noun phrases. Second, ~てくれる ('do for me/us') is a benefactive auxiliary signaling that the action benefits the speaker — '[she] showed it [for my benefit/to my benefit].' Without ~てくれる, plain 見せた would feel cooler, more transactional; the くれた warms it up, registering gratitude. Third, the recipient-marker に on 私 marks who the showing was directed to.