It is the square root function, as in "sqrt(4)" produces the (positive root value) value of 2.
The sqrt(0) -> 0, and sqrt(-1) or of any negative number gives a bad result of 'nan' (not a number).
Therefore, here:
3dcalc -input FILE_IN -expr 'sqrt(a)' -prefix FILE_OUT
every voxel in FILE_OUT contains the square root of the value of that voxel location in FILE_IN.
... but you don't want to have any negative values in FILE_IN if doing that (zero values are OK to have).
--pt