So, what is the Grass-type?
Grass-type is one of the few unique "inventions" of Pokémon. Representing the Chinese traditional element, the Wood, representing the spring, growth, and the Azure Dragon, the guardian of the East. This element corresponds to the traditional element of Earth in the Greek alchemical quartet, while Chinese Earth represents Aether, the divine element.
While almost all traditional RPGs had plant enemies of some sort that were weak to Fire, the popularization of plants as one of the primary elements of nature really started with Pokémon, with other franchises, including THE mother franchise of monster collection, Shin Megami Tensei, following Pokémon's example.
Because Grass-type is effectively an expy of the conventional Earth element, many of the "Nature" based moves, abilities and species are presented in the Grass-type, while actual Earth-type, the Ground-type, takes more inspiration from the Chinese Earth, the substitute for Aether.
The History of Grass-type in Pokémon:
Grass-type's early days are quite weird, indeed. As one of the primary types, it only exist in the starter trio, as neither the Eeveelutions, whose type trio would be reused for the Legendary Beasts, and the Legendary Birds, who represent all seasons except Autumn, had no Grass member. This is in spite of the existence of Leaf Stone, which is responsible for all the evolutions of Grass-types in RBY era, besides Paras-line and the starter. This got even weirder, as while Exeggutor exists as the prime Grass-type and the pre-evolutions in this era were about as powerful as some fully evolved Pokémon, Grass-types were overall weaker than the other elemental types, and gave less experience as well.
This was also present in the moves themselves, as while Grass-type got several status moves, its most powerful moves were Petal Dance and Solar Beam, both of which were incredibly situational and rare. This seems to imply that Grass-type was deliberately meant to be the weaker of the three starter types, focusing instead on status spam and health draining, an aspect exclusive to Grass-type and Bug-type.
In this generation, Grass-type was paired with Bug and Poison, and this organic between them has continued until Generation IV, when TCG put Poison to work with Psychic and Ghost.
The second generation was weirder for Grass-type. With the Special splitting off to Attack and Defense, the bulk of the Grass-types got their Special as Special Attack. However, unlike their Fire-type counterparts, the compensation Defense was much weaker than their original Specials, which gave Grass-types a massive weakness to Fire-types. Because of this, many of the Grass-types turned out much weaker than they were a Generation before, with Exeggutor becoming weaker than Lapras and Arcanine, and Vileplume and Victreebel being some of the weakest fully evolved Pokémon in GSC, and Tangela being only slightly more powerful than regional rodents. The newly introduced Pokémon were also much weaker than the old Pokémon, with Jumpluff being one of the weakest third stage Pokémon in entire game and Sunflora being an eternal joke.
Nonetheless, GSC introduced many things that helped the type. The most obvious one being Sunny Day and Synthesis, with the former being an indirect buff and the latter being much relevant later generations. This generation also introduced Giga Drain, but that would become relevant only in Gen V onwards. Sludge Bomb was another indirect buff, as many Grass-types Poison or non-Poison got it.
The next generation was much more generous for Grass-type. While Grass-types overall kept being weak, some significant Pokémon like Sceptile, Cradily and Breloom managed to become relevant due to their unique characteristics(speed tier, type and Attack+Spore+Priority). With the introduction of Abilities, Grass-types immediately got several type-specific ones, but they were mostly situational. Chlorophyll was the most common one, and Effect Spore was the one exclusive to mushrooms. The rest of the Gras-types however didn't gain such abilities and instead got abilities that were relevant to their habitat like Swift Swim or Sand Veil, relevant to their body type like Suction Cups or daily schedule like Early Bird.
Most influential moves introduced this gen was Ingrain which also inspired the item Big Root and Aromatherapy which solidified Grass-type as a cleric type.
Grass-type got significant changes from the Physical-Special split. Though Grass started off as Special, now Grass-type had a chance to become Physical, which made sense for the type as many of the species members got access to Swords Dance. This shift allowed Tangrowth to become Physically inclined, Flower Gift to provide Attack boost, and made dual offensive Grass-types relevant. However, to accomplish this, several new moves had to be introduced and other older ones had to be buffed.
In addition, new abilities like Leaf Guard, Poison Heal and Solar Power were introduced. The latter two became very relevant... for other types. Grass-types still lacked much beyond what was gained from Gen III on this front.
The fifth generation introduced a lot of Grass-types, most of them being fun to use, but statistically Grass-type remained weak. This generation did not introduce a lot of new Grass-type moves, just Cotton Guard and some other weaker moves. However this generation buffed some older moves like Giga Drain and Petal Dance and made them relevant.
The most significant thing introduced this generation was Sap Sipper, a type absorbing Ability similar to newly retconned Storm Drain and Absorbs. This marked Grass' shift from a weaker elemental type that primarily existed for sake of showcasing to flora to a more conventional elemental type. This generation also introduced Harvest as a new Ability for Grass-types.
This generation was also another okay generation for Grass-types. The newly introduced Grass-types were still not too powerful besides Gogoat, who was far too balanced to be good. Several Grass-types were also buffed to acceptable levels, but many more were forgotten. Most significant thing in this generation was the introduction of Grassy Terrain, a field effect dedicated exclusively for Grass-types, and Energy Ball buff.
This generation continued on making Grass a more conventional type, with new Grass-types getting powerful but gimmicky signature moves and Kartana and Tapu Bulu being introduced. However, sadly, the Grass-types were not buffed too much besides Exeggutor getting slightly more stats. This rendered the most significant introduction in this generation as Leafage, a Grass-type Tackle clone.
The Overview of Grass-types:
For all intents and purposes, Grass-type is a bad type. Not a terrible type, but a bad type. It is objectively the weakest type in terms of offense, defense and stats of all conventional elemental types(besides Poison, which is worse statistically). It remains significant due to its abundance(as the third most common type), and the abundance of its moves, as well as some nifty resistances to Water and Ground
Grass-types' in-universe role is to fill in the flora. That is, to become grass. Their in-game role is generally to work as a good early-game type for dealing with Water and Rock-types. Or to be more clear, work as cleaning paper.
Grass-type's best advantage is, or was, access to sleeping moves. However, with the recent power creep, there is no reason for you to use Sleeping moves, and since most of the Grass-types are incredibly slow, you probably can't in the first place.
Much like Fire-type, Grass-type has little stat boosting moves besides Cotton Guard, which is one of the best stat boosting moves, if only because its users are so terrible. Grass-type is very closely associated with Growth and Swords Dance, the latter largely because most Grass-types have sharp leaves.
Grass-types' niche of absorbing opponent's health haven't been abused by other types, but other types can abuse Giga Drain better than Grass-types, particularly Bug-types, so there is not much reason for you to use them for Giga Drain, or there wouldn't be if Bug wasn't the worst type in the game statistically.