I think 'yang' is like relative pronouns. When describing something in English, you would use relative pronouns like 'which', 'that', 'who', etc. In Indonesian, usually you would translate them to 'yang'. In this sentence, 'yang' emphasizes the description of the noun.

Literal translation: Dia suka kue lembut = she likes soft cakes. Dia suka kue yang lembut= she likes cakes that are soft. Same meaning, slightly different structure.