The sciences division was the corps of officers and crewpeople within Starfleet who specialized in scientific or medical research and control functions aboard starships, on starbases and at Starfleet Command. Members of the sciences division may of specialized in any number of areas including: sensors, research, theoretical and laboratory work, biological studies or trained as technicians, medics and surgeons.
Division colors and uniform
Beginning in the United Earth Starfleet in the mid-22nd century, line officers and non-commissioned officers assigned to the sciences division wore blue division stripes on their uniforms. (Star Trek: Enterprise) By the 2230s, the division was represented by a mustard green color, before switching back to the familiar blue by the 2240s and remaining in place until the early 2270s. During this time, science division officers had a speciality insignia which was included in their assignment patch. (TOS movie: Star Trek; Star Trek: The Original Series)
In the early 2270s, the introduction of a new Starfleet uniform saw the sciences division showing two different division colors. Science research and technical staff wore orange behind their Starfleet badge, on uniform bands, accessories and epaulets. The medical crew now wore green badge backings and accessories. (TOS movie: The Motion Picture)
The division colors were changed once again in the late 2270s, with green continuing to represent the medical personnel, but gray was the new division color for research and technical staff. (TOS movie: Star Trek II: The Wrath of Khan et al.)
By the 2350s the two departments were combined together again and were once again represented by a teal blue color. Uniform styles of later decades would continue to use teal blue as the science division color into the 25th century. (Star Trek: The Next Generation; Star Trek: Deep Space Nine; Star Trek: Voyager; TNG movie: First Contact; ST comic: "Countdown"; ST video game: Star Trek Online)