What is the origin of the Esperanto green star symbol (Verda Stelo)?
The Verda Stelo was created by Zamenhof in 1892 as a symbol for Esperantists.
When asked about this, he said,
"It seems to me, that my attention was drawn to the color green by Mr. [R. H.] Geoghegan and from that time I began to publish all of my works with green covers . . . Looking at one of my pamphlets that I had entirely by chance printed with a green cover, he pointed out that this was the color of his homeland, Ireland; at that time it came to me, that we could certainly look at that color as a symbol of HOPE. About the five-pointed star, it seems to me, that at first Mr. de Beaufront had it imprinted on his grammar [of Esperanto]. I liked that and I adopted it as a symbol. Afterward by association of ideas, the star appeared with a green color."
Note that this quote wasn't sourced, but I've seen this explanation often enough that it seems to be quite likely.
This is a quote from a reputable source.
6.7. Does Esperanto have a logo or symbol?
Yes, there are several. The green star is the oldest and most widely used: it appears on the Esperanto flag, among other places. The colour green stands for hope, and the five-pointed star represents the five continents.