What does it mean to be Jewish?

I know this is one of the largest debates in Judaism, but I want to hear your opinion on it.

In most to all religious ways, I am not Jewish. I have not had a bar mitzvah and I eat non-kosher food, etc. My mother is Jewish religiously and ethnically (both her parents are Jewish, making me 50% Jewish ethnically), and I do partake in the Jewish holidays. I see myself as a Jew. What is your opinion on this?