"The cakes my mother makes are tasty."
A previous lesson states that in case of close relationship (family, company...) it can be omitted
Here 的 is used to create an adjective from all that comes before it. 我妈妈做 becomes the adjective to 蛋糕, which in English can only be translated by something like "the cakes made by my mother" (我妈妈做 的 蛋糕). Remove 的 and you end up saying "My mother makes cakes"
Oops, I answered to the wrong comment. As for the possessive in 我的妈妈, while not wrong it always sounds weird to have many 的 so close to each other in the same sentence. Take out as many as possible and preferably leave juste one is the rule here.
roughly you can see it that way : the cakes 蛋糕 that belong to the category my mother make 我妈妈做. Seeing things that way helps me dealing with wild 的 occurrences.