The horse chestnut is an angiosperm, meaning it is a flowering plant. As I mentioned previously, the flowers of the horse chestnut grow in inflorescences. Each flower produces pollen, which contains the male gametophyte. This pollen must move from the anthers, where it is produced, to the carpel, where the ovary is. The many different ways pollen can be transferred are divided into abiotic and biotic. Most of the methods are biotic, meaning through living animals; the only major abiotic method is wind. However, horse chestnut trees have been known to rely on the wind more than any other factor. They make a large number of flowers, so their pollen is more likely to be spread by the wind. 

When pollen lands on the stigma, the sticky part at the top of the carpel, one of the pair of sperm fertilizes the egg. The other sperm combines with two polar nuclei inside the ovary. Eventually, this will create an endosperm, which will provide nourishment to the growing embryo. Because both sperm are used, this process is called double fertilization.

The fertilized egg, or embryo, will eventually become the horse chestnut seed known and loved worldwide (well, mostly in England). Inside its spiny exterior, the embryo, with the help of the endosperm, becomes a hard, round, shiny conker. The main methods by which angiosperms disperse their seeds are wind, animals, and water. Because the horse chestnut seed is very large and heavy, wind is ineffective in dispersing it. So, unless a horse chestnut is near a body of water, it will spread its seed through animals.