A stór is a term of endearment. It literally means store, in the sense of 'thing of great value'.
The A before the noun is the vocative particle 'a', which puts the noun into the vocative case.
The endings of male names and masculine nouns are generally palatalised in the vocative case but this does not occur in certain terms of endearment, including this one.
A variation using the diminuative, stóirín, is also common in naturalistic speech.
A stór and a stóirín are often — though by no means always — used to convey an affectionate romantic or parental subtext.