An Imaging Spectrometer is a Spectrometer that collects spectral data over a two-dimensional area, i.e., for each part of the image, information about the Intensity for each Wavelength is determined. This produces a "cube" of data (three dimensions), two being spatial (the image) and one being the spectral data at the specified point.
There are various types: a common type for astronomy is the Integral Field Spectrograph which incorporates a device called the Integral Field Unit (IFU) to arrange pieces of the two dimensional image along a line, i.e., one dimension. Common spectrometers use a slit to image and measure the spectrum across a line selected from the telescope's two-dimensional image, so the resulting graph (photo or electronically stored image) displays spectral data in one direction (the Spectral Direction or Dispersion Direction) and spatial information in the other (the Spatial Direction). By the rearranging, the same Spectrograph can capture spectrums of the whole image at a lower spatial resolution. Lenses, prisms, and/or fiber can be used to accomplish the rearrangement. This constitutes a time-saver compared to taking a series of snapshots with a "normal" spectrometer, shifting the slit each time to capture two spatial dimensions.
Another type is an Imaging Fourier Transform Spectroscopy (IFTS).
Be warned that spectrographic instruments may offer the option of bypassing the prism or Grating, so as to use its camera for (non-Spectroscopy) imaging. Such an instrument may be described as an "imaging spectrograph" (e.g., the Hubble Space Telescope (HST)'s STIS) even though in spectrograph-mode, it views only the typical long-slit single dimension.
CCAT Prime (CCAT-p)
Chandra X-ray Observatory (Chandra)
Mars Reconnaissance Orbiter (MRO)
Position-Position-Velocity Space (PPV)
Solar Maximum Mission (SMM)
Thirty Meter Telescope (TMT)
James Webb Space Telescope (JWST)