She laughed to hide her fear.

Literal

She [topic-は], fear-feeling [object-を] hide [in order to-ために] laughed.

~ために in its purposive sense ('in order to X') links the laughter to its goal — concealing the fear. 恐怖心 ('fear, sense of fear') uses the suffix ~心 ('mind, feeling, heart') to nominalize an emotion: 恐怖 alone means 'terror,' but 恐怖心 emphasizes the inner felt experience. Same pattern: 好奇心 ('curiosity'), 自尊心 ('self-respect'), 独立心 ('independent spirit'). Forced laughter as fear-management is a universal human strategy, but the careful, clinical phrasing here gives it an observational tone.