The James Webb Space Telescope Science Working Group has developed the Science Requirements Document in order to describe the scientific objectives for the JWST mission and the performance capabilities necessary to meet them. The primary objectives fall into four science themes that span many orders of magnitude in time, space, and size.
The basic science objectives of JWST are also described in Gardner et al.
WebbTelescope gives a "down-to-earth" description of JWST, including the advantages of observing in the infrared part of the electromagnetic spectrum. Numerous videos, animations, and education material are available for download.
A more extended description can be found at the JWST Science Goals web pages of the Goddard JWST Project Center. Guidance on the science goals and capabilities of JWST is provided by the Science Working Group (SWG).