Final answer:
The gametophyte is the structure in ferns that produces sperm and egg cells through the reproductive organs called antheridia and archegonia, which are part of the haploid phase of the life cycle.
Step-by-step explanation:
In ferns, the plant structure that produces sperm and egg cells is known as gametophyte. The gametophyte contains reproductive structures called antheridia (which produce sperm) and archegonia (which produce eggs). These structures enable the production of gametes under the haploid phase of the fern life cycle. Precisely, the antheridia release sperm with flagella, allowing them to swim to the archegonia where they fertilize the eggs.
The resulting zygote will then develop into the diploid sporophyte, which is the dominant and visible part of the fern's life cycle. Importantly, all the cells of the gametophyte, and thus the gametes, are haploid; thus, they are not produced by meiosis, as they are already in the single set of chromosomes (n) state.