This racial bonus improves the Planet quality of your planets.
- Green Thumb (+10%) cost: 3 points
- Magical (+20%) cost: 8 points
It gives more green tiles on planets. However the bonus is always rounded down, limiting its effectiveness somewhat.
Slightly more useful in DL where a planet gets TWO new terraforming tiles if it is class 15+, and 3 if it is class 25+. That effect is not present in DA or TA.
High quality planets get a bonus to their approval. In TA the bonus is a flat +10% added at the end if Class 11 or higher, and so would only come into play on Class 10 worlds. (Green Thumb lets races with a Class 10 homeworld get the bonus from the start, which can be powerful on smaller maps.)
The extra improvements across your empire can be used for Economics and Morale buildings to bring in almost as much tax as choosing the Economics Bonus (albeit at twice the point cost) -- or, for extra manufacturing/research/influence/etc instead, as needed, making this a less efficient but more flexible alternative.