As a member of a family whose members have been saying that for three generations, I can speak with some authority.
It means, "I don't believe in the existence of gods or a god." There are no implications about evidence or the lack of it, and there's certainly no ambiguity. I was raised in a home where the existence of a god was never discussed, any more than your parents would have brought up the possibility of the existence of Klingons. I was about seven when one of the kids at school started talking about a god, and I laughed uproariously because I quite reasonably assumed he was joking.
It was many years before I got a glimmer of understanding of how and why adults could believe in such a fairytale. By then I was taking science classes in high school and had some comprehension of the scientific method. I was finally able to put my skepticism into words: How can you believe something for which there is no evidence? Wouldn't it be just as "reasonable" to believe that a bucket of money will fall out of the sky and land in your yard?
It was decades later that I learned the Rule of Laplace and was able to defend my skepticism: Extraordinary assertions must be accompanied by extraordinary evidence before anyone is obliged to treat them with respect, so I choose to exercise my right to not treat this most extraordinary hypothesis with respect.
