What defines being a "legacy"?

Ignoring uncles, cousins, siblings, etc., what makes you a "legacy" to a certain college? I'll put this in context of myself, because keeping it hypothetical is too much work.

My father got his bachelor's from Cornell, and his master's from Boston U. However, despite the fact that the degree reads BU, he did most of his studying at NYU. My mom got her bachelor's from the University of Vermont, her law degree from Duke, and her MBA from NYU. My other (step) dad didn't complete college, but went for a few semesters at a UC (I don't remember which one). My father's girlfriend (very long-term) got her bachelor's from Boston College and her MBA from NYU.

I'm obviously a legacy from Cornell and UVM, but what about Duke or BU? Am I a legacy from NYU, and if so, whose degree counted for that? Am I actually a legacy from Boston College or that one UC?

Also, if my father with his bachelor's from Cornell didn't give that much money, but my mom with her law degree from Duke always gave whatever donation was asked for, whose legacy status would likely count more with the admissions people?

Based on what you said here, it seems like the only schools where your legacy status would be relevant in the undergraduate admissions process are Cornell and UVM. The schools where your parents earned professional degrees will probably not consider you a legacy in the undergraduate admissions process - college as an undergrad and college as a grad student are two very different things. If your stepdad didn't graduate from the UC, then you wouldn't technically be considered a legacy there either. With your dad's girlfriend it's a little harder to say; it depends on whether she's considered one of your legal guardians or not.

Despite the fact that your dad contributed very little to Cornell, for undergraduate you will still have a stronger legacy status there. If you end up applying to law school, however, the fact that your mom donated a significant amount to Duke might give you even more of a leg up in that scenario.

Overall, I would try not to worry too much about whether you're a legacy at all these schools. It will only make a minor difference if any at all. Focus on getting your grades and scores up to the level where you'll have a good chance of getting in legacy or not!