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.

Hi Kate, "Mermaid pearls" are a type of pearls. In this case, the word "mermaid" is an adjective distinguishing the specific kind of pearls from other kinds. "Mermaid's pearls" means the pearls belong to the mermaid. In this case, "mermaid" is a noun, and the apostrophe-s indicates ownership of the pearls. Now I'm not a jewelry expert. I'm only answering this question from a language perspective. If someone who knows more about jewelry has a better answer, please listen to him/her.

Thank you all who responded!

Mermaid's pearls are pearls that belong to a mermaid. 'Mermaid pearls,' has no specific meaning that I know of - it implies that the pearls look like a mermaid. You should not omit the 's,' if you mean that something belongs to somebody.