This "synonyms thing" as it pertains to parent plants can be confusing. Evan is right to call them synonyms but they are actually not synonyms in the botanical sense.
So here is the definitive answer to how this works:
A parent plant is created. Which plants are the children to that entry is determined by the name of the parent plant.
1) So, if the parent plant has a genus with no species, then every orphan plant (that is, plants with no parent yet) become a child plant to that parent.
2) Now, if you want to get more specific than that, then you create the plant with a genus AND a species. And then it'll match any child plants that have the same genus and species.
Now, what if you want the plant to match more than one species, but not all of them? This is where you utilize the synonyms field.
So, let's pretend you have genus "Foo" and species "alba", "indica", and "vulgaris" and you want your parent plant to only match the first two. You would make the parent plant be:
Genus: Foo
Species: alba
Synonym: Foo indica
Now, as a side note at this point, you can make that parent plant be a parent to other plants that are not in the same genus. So you could add another synonym at this point, called:
Synonym: Bar vulgaris
And now the parent plant is a parent to:
Foo alba
Foo indica
Bar vulgaris
