A common example of a multispectral imager is color TV. A color TV splits
the incoming light into red, green, and blue channels. 
In
a color TV dichroic beamsplitters split the light into its component colors
which are then directed a focal plane array (FPA) for detection.
An ideal astronomical imager would split the incoming light into multiple
spectral channels. A typical astronomical observation might consist of
standard photometric band-passes such at those shown here:
Note that real filters are not 100% efficient - filters suffer reflection
losses and light is absorbed in the filter substrate and coatings. For
three channels the color TV approach might be practical, but frequently
many more than three channels are needed. For example, the
Hubble
Deep Field was observed sequentially with a single FPA and four filters
centered at 300 nm, 450 nm, 606 nm, 814 nm. Spectra used to measure redshifts
typically have hundreds or thousands of channels, in which case it becomes
impractical,
inefficient, and inflexible to use hundreds of dichroics and FPAs.
In contrast, an imaging Fourier transform
spectrometer is practical, efficient, and
flexible.