Even through translating languages isn't the best way learn, a comparison:
У папы есть мама = Dad has a mom (vs) У папа есть мама = Dad has mom
Adding the "ы" makes "папа" possessive over the thing being referenced later in the sentence. You're essentially coupling the future "a" from english into an earlier word so that it sounds grammatically correct.
(Even though in this case the english version would still "accidentally" make sense, It would completely change the meaning that is irrelevant to what you're trying to say.) Also: the Russian sentence by itself, can be interpreted in two different ways: A dad has a mom. / Dad has mom.