Gametes, sporophyte, gametophyte, and zygote. explain how the terms are related.

These terms represent the stages that occur in alternation of generation. Alternation of generation describes the process in the life of some eurkaryotes [mostly plants and protists], it refers to the alternation in form which occur in these organisms. One form is usually diploid with 2n chromosomes, this is called the sporophyte while the other form is haploid with only one set of chromosomes and it is called the gametophyte.
The spores go through mitosis and produce gametophyte, the gametophyte produce gamete. Two gametes fuse together to become a zygote.

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