The Connecticut State Seal is adorned with a trio of grape vines. Appearing below the the grape vines is a banner with the state motto: "Sustinet Qui Transtulit" (Latin for He who is transplanted still sustains). "Sigillum Reipublicae Connecticutensis" is Latin for Seal of the State of Connecticut.

The original seal had 15 grapevines - brought from England in 1639 by Colonel George Fenwick and used as the seal of the Saybrook Colony (the Saybrook Colony was established in late 1635 at the mouth of the Connecticut River in what is today Old Saybrook, Connecticut):

The map above shows the Connecticut, New Haven, and Saybrook colonies from 1636-1776. It includes the territorial disputes between Connecticut and its neighbors during that time period (purple shading). It does not show Connecticut's western land claims and dispute with Pennsylvania. The map is based primarily on descriptions from The Boundary Disputes of Connecticut by Clarence Winthrop Bowen. James R. Osgood and Company, Boston, 1882 (larger, more detailed version on Wikipedia.org).

Source:

The State Seal - Great Seal: Connecticut official website
Saybrook Colony: Wikipedia.org

Links:

State Seals - 50 States List
National Seal