The definition I gave is the quickest and least complicated definition of saturated vs. unsaturated fat that I can give to a layperson. I find that when I start getting into the level of detail that I had to learn about the subject (since I'm a PhD life scientist), people don't understand and I lose them. Of course, the actual chemistry of fats is far more complex than a simple test of whether the fat is solid at room temperature.
I admit my eyes did glaze over when I was reading on the chemistry of saturated vs unsaturated fats and single bond vs double or triple bonds of carbon atoms. The diagrams were not something I could ever commit to memory. But I can grasp the gist of it. Even us lay people sometimes have occasion to come across the more detailed explanations.