JWST is the top scientific priority of the 2001 NRC Astronomy Decadal Survey, Astronomy and Astrophysics in the New Millennium", and is the foundation upon which the 2010 NRC Astronomy Decadal Survey, New Worlds, New Horizons in Astronomy and Astrophysics", was built. The core science themes of JWST are 1.) The End of the Dark Ages: First Light and Reionization, 2.) The Assembly of Galaxies, 3.) The Birth of Stars and Protolanetary Systems, and 4.) Planetary Systems and the Origins of Life.
Similar to other Great Observatories such as the Hubble Space Telescope, JWST will impact many themes that are at the forefront of astronomical research today. At one end of the spectrum, the science case includes tracking and observing planets, moons and Kuiper belt objects in our own solar system to understand its early formation history. At the opposite end of the spectrum, JWST will find the most distant supernovae in the Universe to measure its expansion and test models of dark energy. The JWST Science Working Group (SWG) and other scientists have written several white papers describing key science cases that JWST will tackle.
The Space Telescope Science Institute (STScI) is the science and flight operations center for JWST, and has played an important role in defining the science goals of JWST. A detailed Science Operations Design Reference Mission (SODRM) was prepared to guide the development of the Science and Flight Operations Center. It is based upon the JWST science requirements and goals as defined by the SWG, and includes a set of hypothetical observing proposals that define a core science program for JWST. This program is analyzed to carry out operational studies. This article contains more information on the science requirements. The SWG provides NASA guidance on the science goals and capabilities of JWST. STScI supports the SWG and has two participating members (ex-officio and selected).
An earlier Design Reference Mission was developed by the Ad-Hoc Science Working Group, one of the forerunners of the current JWST SWG. The new 2012 Science Operations Design Reference Mission (SODRM) is available here.
If you would like to know whether your observations are going to be feasible with JWST, you should look at the JWST Prototype Exposure Time Calculators or the Sensitivity page. We also present JWST science simulations, which are part of the program to investigate feasibility of JWST observations.