This large torii was modeled after a similar one at the famous Itsukushima Shrine in Miyajima. The sign says "Dai-Myojin" which simply implies that this is a large torii of the Myojin style (torii with a curved kasagi). Technically though, this is a Ryobu style torii, a type of myojin torii that has support posts on each side.
Designed by Takeo Shiota (1881-1943) in the early 1900's, the Hill-and-Pond Garden at the Brooklyn Botanic Garden is three acres of Japan hidden in New York City. The variety of plants, large pond, pavilion, lanterns, small shrine, and large torii fit wonderfully into the overall design.