An integral field spectrograph (or integral field spectrometer) combines spectrography and imaging, producing a "cube" of data (three dimensions), two being spatial (the image) and one being the spectral data at each specified point. Its use is called integral field spectroscopy (IFS).
It is commonly a "normal" spectrograph plus an integral field unit. A "normal" spectrograph collects data from a narrow line-like area rather than from a two-dimensional area, offering spectral data over one spatial dimension. The integral field unit rearranges points of light so that the slit includes data across a two-dimensional area, paying for this capability by lowering the spatial resolution. Spectrographs are often built so they can be used with or without the integral field unit.
Methods used: Image slicer directs light from different parts of the image into a slit such that parts of the image across two dimensions are all fed through the one dimension of the slit width. UVES of the ESO VLT does this.
Lenslet array has a lens for each pixel. SAURON of the William Herschel Telescope (WHT) uses this.
Fibers uses optical fibers to direct the image into a single slit. INTEGRAL, used on the WHT uses this.