Question from someone who is not Jewish

I’m not familiar with Judaism entirely, though I’ve always felt drawn to it and interested in it. Please let me know if I describe things the wrong way or using the wrong language. I’m trying to learn and appreciate the help.

I’ve come across discussions on reddit talking about interfaith marriage. And someone explained that if a Jewish man had children with a non Jewish woman then the children wouldn’t be Jewish?

It made me curious because: I have a great grandmother on my mother’s side who was Jewish but she married into a Christian family. I’m a woman. So if the culture is passed on down the matrimonial line does that mean I’m Jewish? Or am I 1/16 Jewish? Or am I not Jewish at all? If I had children with a man who was Jewish, would that mean my children would be Jewish?

Sorry if I’ve worded this in a bad way. I’m not sure if there’s a more appropriate way to explain my question. But I’d appreciate your input 🙂