Nature Day is an event in honor of the general greenery in the player's town.
In Animal Crossing
In Animal Crossing, Tortimer will give the player some advice about nature if he is spoken to. He will also give the player a Tree Model.
In City Folk
In City Folk, Tortimer will give the player a Cool Globe if they speak to him outside the Town Hall by the end of the day.
In New Leaf
In New Leaf, Isabelle will be celebrating the Nature Day by the Town Tree. There will be a standee over there and she will give the player a Cool Globe.
In New Horizons
In New Horizons, Nature Day takes place from April 23rd to May 4th, featuring special Nook Miles+ rewards for nature-related activities (such as planting bushes), as well as more frequent visits from Leif, who sets up a stall in the Resident Services plaza.
After completing a Nature Day-specific Nook Miles+ task for the first time, the player can speak to Tom Nook in the Resident Services building to receive the HedgeDIY recipe.