This is an interesting question because students usually ask about using red, blue, or green light to grow plants. I have never heard that purple light would be good to grow plants, but I'm guessing it's good because purple is a mixture of red and blue. Let me tell you why red and blue is important. It all has to do with understanding the visible light spectrum, or a rainbow.

Light is absorbed and reflected. The color that is absorbed is not the one that is reflected, and the reflected color light is the color of light we see. The rainbow is all of the colors of light that the sun emits. When we see white light, it is a mix of all of these colors. So how does this relate to plants? Well, plants are usually green, such as their stems and leaves. Those parts of the plants that reflect off green light (the color we see) absorb all other colors of light except green. If they absorbed green light, another color would reflect and we wouldn't see plants as green.

Now, a plant's green leaves are the sites of photosynthesis. Photosynthesis is when plants capture the light from the sun and convert it into food for themselves. Photosynthesis mostly happens in the chloroplasts of the leaves. The chloroplast has photopigments which absorb all of these colors of light from the sun that shine on the leaves (except green). Every photopigment is color specific and absorbs only the color is it meant to absorb. Plants primarily absorb red/orange and blue light.

So now you can see why purple light might be good for growing plants. A plant uses light to make food, the food the plant makes from using light helps it to grow, and the photopigments in the chloroplasts primarily absorb red and blue light. Red and blue mixed together is purple!