As viewed from a disant solar-type star, Jupiter (which is 5 times as far away from the Sun as the Earth is), would be about a billion times fainter in visible light than the star. It is not merely the difference in brightness which causes difficulty in imaging extrasolar planets, but diffraction of the starlight by the telescope. Much of this light spreads out in the image-plane where planets would be found, preventing detection.
It is the giant Jupiter-like planets that are currently being detected by ground based observers using [Doppler techniques]. However, almost all of these objects are much closer to their stars than Jupiter is, and nearly all orbit their stars closer than the Earth orbits the sun. Several of the Doppler detected planets about nearby stars (Upsilon Andromeda, 47 Ursa Majoris, GL 614, & Epsilon Eridani) could be directly imaged using even a low-performance occulter screen.
External occulter space missions have several advantages over other types of coronagraphic designs. Since the occulter is not built into the telescope as an add-on instrument, scattered light is reduced before reaching the telescope. There are no unwanted diffraction spikes resulting from coronagraph supports, and the complexity of telescope optics and internal instruments is reduced. Some of the difficulties with conventional coronagraphs are the result of small scale imperfections in manufacturing and materials, and these are avoided with an external occulter.
An external occulter can move while the science instrument is fixed on a background target. The target of interest may be placed anywhere in the image plane of any science instrument, unlike in conventional coronagraphs. All science instruments can be used with an external occulter--imaging arrays as well as spectrographs. The study of extrasolar planet properties, photometrically and spectroscopically, could be achieved.
In simple terms, external occulters uses the oldest trick in the book: blocking out glare. We do it with sun-visors in our car, or with our hand when we look up on a clear-sky day near the sun to see birds or planes flying overhead. You can even use the technique to help see Venus near quadrature during the daytime if you know where to look (and are blessed with a clear atmosphere).