The genus, Trifolium, was named for its typical three-leaflet leaf, repens means creeping. There is wide variation in white clover. Varieties can be found with all green leaves, green marked with red or red and white chevrons, and almost all red leaves.
'Good Luck' is a unique variety. White clover plants will occasionally throw up a leaf with four, five, or more leaflets. (I've found clover leaves with as many as eight.) It is considered lucky to find the odd four-leafed among all the others on a plant. The 'Good Luck' variety is selected for its ability to produce extra leaflets.
In temperate areas, white clover was once an old stand-by in lawns planted in a mix with grasses like rye or blue. The roots have a symbiotic relationship with bacteria that 'fix' atmospheric nitrogen making the nutrient available to the clovers and nearby surrounding plants. Used in pastures as a forage plant, white clover has been declared a lawn weed.
The logic of this 'declaration' escapes me. White clover seldom needs watering and fertilizing, makes a short ground cover, prevents erosion, has few insect pests, rarely needs mowing, and makes a beautiful textured lawn. Perhaps that is why it has been 'sold' as a weed--it reduces sales of fertilizers, pesticides, and lawn mowers.