What are characteristics of "high quality" graduate research as viewed by a hiring committee?
Ultimately quality is a judgement call that every reader gets to make. 

For example, a paper in mathematics might be considered to be "high quality" to half a dozen people worldwide who happen to be interested in the main result of the paper (or other work). Especially if the question has been open for a while. But other mathematicians may just say "meh" because that result neither interests them specifically, nor advances their own studies. 

Reviewers at journals and conferences need to be able to make such judgements and, generally, they do a good job and we respect those judgments when we find published papers. But not everything that is published is of high quality. 

But, some of the criteria that reviewers and others will use are as follows. 

Is the solution correct? And reproducible?

Is the problem long standing? Or does it break new ground?

Does it open new areas of research? 

Is it novel in some sense? Or just an easy derivation from what is already known? 

Could I have done this easily? Or does it surprise me in some way? 

Is the result widely helpful to either researchers or society as a whole? 

Note that all of the above are judgement calls and all imply some scale with, not interesting at one end and very interesting at the other. 

But I think the real intent of what you have read, is that it is more important what you do in your research than the general reputation of the place in which you do it. Reputation is based on many things, not all of which are directly relevant to the quality of research. In particular some places that seem quiet generally may be hotbeds of ideas in some niche of some field. 

And note that hiring committees may rely on the judgements of others, such as the work being published. They might also rely on just the judgements of writers of letters of recommendations if those writers themselves are in a position both to know and to be honest. But they might also, in some cases, rely on their own judgement. "Well, yes, this is interesting, but not interesting to us at this time."