Translation:She is eating breakfast because she is hungry.
It is informal, but it's very common used, it is even in Cambridge dictionary (last example):
There are two ways of use it in informal way "cause" and "'cause" and I don't really understand why it would be wrong or not proper English.
the word cause is a proper word, but using cause instead of because is not. In spoken english, yes it's common. In written, no. Even those who do would add an apostrophe in front ('cause), but you would never see that in a newspaper for instance. People don't write the way they speak though.