The normal functioning of a CCD, astronomical or otherwise, can be divided into two phases: exposure and readout. During the first phase, the CCD passively collects incoming photons, storing electrons in its cells. After the exposure time is passed, the cells are read out one line at a time.
During the readout phase, cells are shifted down on the entire area of the CCD. While they are shifted, they continue to collect light. Thus, if the shifting is not fast enough, errors can result from light that fall on a cell that was not in its proper position. In addition, the CCD cannot be used to collect light while it is being read out. Unfortunately, a faster shifting requires a faster readout, and a faster readout can introduce errors in the cell charge measurement, leading to a higher noise level.
A frame transfer CCD solves both problems: it has a hidden, not normally used area contaning as many cells as the area exposed to light. When the exposure time is up, the cells are transferred very rapidly to the hidden area. Here, safe from any incoming light, cells can be read out at any speed one deems necessary to correctly meausure the cells' charge. At the same time, the exposed part of the CCD is collecting light again, so no delay occurs between successive exposures.
The downside of such a CCD is the higher cost: the cell area is basically doubled, and a more complex control electronics is needed.