Like ripples in a pond, as we move through life we have an effect on the environment around us. I love this phrase because it's a simple reminder to eschew consumerism, protect the environment, and be conservation minded.
The specific phrase "Live Lightly" comes from the book Lightly by Francine Jay. Which is awesome. I know Marie Kondo gets all the buzz in this space and I've read herstuff. But I really liked this one.
To quote from the description on Amazon:
There's no shortage of decluttering books on the market, but Lightly is different. It goes beyond decluttering - far beyond - to uplift your thoughts, your actions, every moment and aspect of your life.
You should read it.
Another awesome book, and the one that kind of turned me on to the minimalist concept, is Essentialism by Greg McKeown. Essential reading in my opinion. ;-)