The construction 'A + 's + B' means that the B belongs to the A. For example, 'the dog's food'. If you say 'Don't eat that! It's the dog's food!', this means that this is the food which belongs to a specific dog. It's not my food or your food - it's the dog's food.
With the compound noun A+B, this tells you what kind of 'B' it is. The noun 'A' makes the noun B more specific. For example, 'dog food' is a type of edible product intended for dogs rather than cats, rabbits or humans. Compound nouns are extremely common in English - a winter coat is a type of coat intended for use in winter, a wine glass is a type of glass intended for drinking wine from, and so on.
A mermaid pearl is a type of pearl.
A mermaid's pearl is a pearl that belongs to a mermaid.