E.g. what the light or sound spectrum is, what it's useful for - in very simple terms that a grandmother or a child would understand.
I would start with talking about music - piano, a capella choir, etc. Why thirds and fifths and octaves sound good, but seconds don't.
Then maybe move on to the radio dial, eventually moving on to light and prisms.
To a child you have to show pictures.
A diamond in your ring or a wedge of glass or crystal, then the Sun light, or ..
Play and record two notes at the same time in a piano (or software app) and then one at a time, and then apply FFT and show her the results.
I would use the idea of explaining the spectrum of light by relating it to the spectrum of flavors. Surely children and grandma must have tasted a variety of flavors in their life time. You can use different flavors, (salty, sweet, bitter, savory, sour, super sweet, super salty, super bitter, super sour, whatever you can think of, etc) to represent the different parts of the flavor spectrum.
I would then describe how different dishes of food lie in different places in the spectrum of flavors. Dessert like ice cream would fall under the spectrum of sweet. There are super sweet desserts, strawberry short cake, and there are more bland desserts such as pound cake. By establishing a point of reference in which the student can relate to and is extremely relevant in their lives, (food the most common thing.) They feel a connection. It is important to have this kind of connection before you start talking about colors. If you immediately start talking about colors, they might not have/feel immediate pleasure from it. When talking about food, it definitely brings about a state of mind that feels good.
After establishing the idea of a spectrum of flavors, you can explain to a child or grandma that they must have seen different colors of light! At this moment, the child or grandma will understand that you are trying to relate a range or "spectrum" of flavors to the range or "spectrum" of light. At this point, start describing about how you can mix colors together and how mixing colors is like mixing different flavors in a dish of food.
There are so many varieties of food, talk about their favorite food and what flavors it has in it!! By tasting the food, you are doing "flavor spectral analysis" Explain how food critics are like spectral analysis machines that are bias, LOL.
The most important thing to do is to keep it simple. This does not necessarily mean to dumb it down. Try to focus on one or two things you want them to understand, the idea that there is a range of colors/flavors and that analyzing a food dish and trying to find out its recipe is what physicists are try to do with a spectrum of light. Make sure to work off of the feedback they give you. And don't get discouraged, because you don't want them to remember you as the person who gets frustrated whenever you try to talk to them.