How does the whole sporophyte/gametophyte generations thing work? This just does not make sense to me...

Answer:
A mature sporophyte produces spores by meiosis, a process which reduces the number of chromosomes to half, from 2n to n. The haploid spores germinate and grow into a haploid gametophyte. At maturity, the gametophyte produces gametes by mitosis, which does not alter the number of chromosomes.
Explanation:
hope this helps!