So, what is Grass-type's role, really?
The Legendaries and Their Role:
Admittedly, I didn't research on these guys so much, since there is no mascot legendary that is a Grass-type(Xerneas is arguably a honorary one though)
Celebi's time travel abilities seem to be a reference to the Time Capsule. Its body shape is based on a generic tree sprite, while its association with the Ilex Shrine likely refers to kodama in Shintoism. Its ability to being eggs from future also likely refers to breeding being introduced in Gen 2.
Shaymin seems to be personification of the concept of gratitude, and its domain's name seems to imply that it is largely based on religious gratitude. Its ability to detoxify the land alludes to Suicune and seems to be personification of Aromatherapy the move. Its Sky Forme likely refers to messengers of gods.
Based off Hawaiian God Lono, Tapu Bulu seems to represent the "Revenge of the Gaia", that is, flora taking back their land from humans as a punishment for humanity's mischief.
Based off Aramis of the Three Musketeers, Virizion primarily appears a guardian for forest based areas.
The Trainers and Their Roles:
With the tile of "Nature-Lowing Princess", Erika more or less represents traditional Japanese gardening. Though Bellossom seems to be her signature Pokémon GSC onwards, she traditionally doesn't have much difference between her Bellsprout-line members and Oddish-line members. Tangrowth also appears as her signature in HGSS rematch, though Vileplume rereplaces that in B2W2, with Bellossom getting the shaft.
With the tile of "Master of Vivid Plant Pokémon" and her green hood, Gardenia seems to based off an archetypical forest hiker. Her signature is Roserade.
Cilan serves as the meekest of the three Straiton Brothers, often failing to complete his sentences. His signature is obviously Simisage.
Ramos' title is "The old growth is still in bloom!"(Japanese version is not a full sentence, obviously). He doesn't have much of an interesting personality, but he makes plant puns. His signature is Gogoat.
The Trial Captain of Lush Jungle, her trial involves cooking. She based off a generic animé bad cook, someone who is relatively hyper but not too serious about the taste. Her signature Pokémon is Steenee, her Mega in Battle Tree is Sceptile and the Totem Pokémon of her trial is Lurantis.
Her extra story in Moon reveals she intends to follow in her father and brother's footsteps. INB4 Bechdel test.
The Overview:On the legendary side, most Legendaries seem to be associated with forests, with the exception of Shaymin who is based off flower beds. Nonetheless, all of them represent the divinity of the untouched nature in some manner. Most of them appear as guardians of sorts, with few of them having to do with fertility.
On the trainer side, most trainers associated with the type are associated with either gardening or cooking, with the partial exception of Gardenia. Almost all of them are mellow, carefree trainers, with Mallow being the most hyper of them. They seem to be wiser than most trainers, but not necessarily deeper. They seem to be willing to give their knowledge freely to others. Some of them seem to be quite lazy as well, another characteristic of the type's species.
Since Grass-type hasn't been an E4 or mascot legendary type, it is hard to say what it would represent in those roles.