* spora (σπορά) meaning "seed" or "sowing"
* phyton (φυτόν) meaning "plant"
Therefore, sporophyte literally means "seed plant".
This name is fitting because the sporophyte generation in plants is the diploid generation, which produces spores through meiosis. These spores then develop into the haploid gametophyte generation, which produces gametes (sex cells).
The term "sporophyte" was coined in the late 19th century by botanist Wilhelm Hofmeister, who was studying the life cycles of plants and the alternation of generations.