A spectral index is a mathematical equation applied using the spectral bands of an image.
Satellite images are composed of bands. An index can compare and contrast these bands to give insights into things like photosynthesis in plants, vegetation density, or the location of recent forest fires. Spectral indexes can also be used for machine learning and deep learning.
Different satellites collect different bands. Check the capabilities of the chosen satellite and what bands it gathers in order to know whether you'll be able to use the indexes you want with its images.