The Earth Sciences Institute was a organization designed for exploration and scientific discovery on Earth.
The A-6 Excavation Team which studied the debris from a Borg sphere found in the Arctic Circle in 2152 was from the Earth Sciences Institute. (ENT: "Regeneration")
The Earth Sciences Institute was never mentioned in dialog. The name comes from an assignment patch worn by the A-6 Excavation Team.
The Science Counsel may be associated in some way with the Institute, since the A-6 team checked in with them.
Members
There could be further member of the Institute in the forth person seen onscreen with the A-6 team, who wasn't named on the assignment patch, or the three to five extra Human lifesigns on Arctic One when it was first encountered by Enterprise.