I'm not familiar with the term, but intuitively it would seem to be a 'mixture' of white box and black box testing, since those terms are pretty much 'binary'.
Either you know what is 'in the box' (white) or do not know (black).
So, I postulate that 'grey' would be doing both types of testing (seems redundant), or doing part of the testing black and part white, or having some 'black' boxes inside a bigger 'white' box.
John