I hope you get several explanations from different people.
My understanding is that (although it can have precise technical meanings depending on context) the term expresses a GENERAL IDEA and the root analogy is with image processing.
in photography you can have fine grain film (small pixels) and coarse grain film (large pixels)
and you can take a finegrain image and progressively coarsen the grain
until finally it might look like one of those pictures made of greytone squares on a graphpaper grid. it can be so coarsegrained you cant recognize it except you hold it out some distance
As if you lay graphpaper tracing paper over something and in each square you average the greytone so it is uniform within that square
you end up with a crude matrix of numbers which tell the greyscale in each pixel
IN COARSEGRAINING SOME OF THE MICROSCOPIC INFORMATION IS ELIMINATED or averaged out so that you end up with MUCH FEWER NUMBERS DESCRIBING whatever it is.
So the ultimate coarsegraining in THERMODYNAMICS where you just know really gross degrees of freedom like "pressure" "temperature" "volume"
and you CANT SEE the antheap of activity inside the gas with all the molecules whizzing crazily around, all that microscopic information has been washed out or erased and summarized by 2 or 3 coarse variables.
And with a black hole the HORIZON does the coarsegraining for you because there may be millions of things happening inside related to gravitational collapse but you never see that, all you supposedly see is the area and temperature of the event horizon, and whatever diddly Hawking radiation is percolating out. it's very coarsegrain.
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