The following are general definitions from an American Jurisprudence piece. I just did a quick copy and paste job with it for the board's consumption. Note that "injury as a result thereof" is one of the key elements in a couple of the definitions. I suspect that's where Hillary's escaping indictment on this one. I don't know that, but that seems most likely. Remember, if all the elements are not there, then it is not X crime. And that matters. Or to put it the way they tell you in law school, it's like a chocolate chip cookie, if it has everything except chocolate chips, it isn't a chocolate chip cookie. This could also go to 5th and 14th Amendment protections but it's not really necessary since the case has likely ended here. 
I'll also add that terms like "ordinary care" and "lack of diligence" and similar terms all open up cans of worms for the prosecution. Finally, there can't be any on-point case history/precedent for this. If anything, the case history likely shows they'd fail miserably if they tried the case. The FBI did not fail to speak with a platoon of lawyers about this before deciding to not recommend charges. Enough smart people told them they had nothing and that's the reason for the recommendation. 
V. Degrees of Negligence; Willful and Wanton Acts
A. In General
2. Definitions
b. Gross Negligence
(1) In General
Topic Summary Correlation Table References
§ 227. Generally
Observation:
In gross negligence, the element of culpability which characterizes all negligence is magnified to a high degree as compared with that present in ordinary negligence.1
West's Key Number Digest
West's Key Number Digest, Negligence Key Number Symbol273
Forms
Complaint, petition, or declaration—Allegation—Gross negligence. Am. Jur. Pleading and Practice Forms, Negligence § 130
Motion to dismiss—Provision—Failure to show gross negligence as against one of several defendants. Am. Jur. Pleading and Practice Forms, Negligence § 132
"Gross negligence" is a nebulous term2 that is defined in a multitude of ways, depending on the legal context and the jurisdiction.3 
"Gross negligence" is commonly defined as very great4 or excessive5 negligence, or as the want of, or failure to exercise, even slight6 or scant7 care or "slight diligence."8 
"Gross negligence" means more than momentary thoughtlessness, inadvertence or error of judgment;9 hence, it requires proof of something more than the lack of ordinary care.10 It implies an extreme departure from the ordinary standard of care,11 aggravated disregard for the rights and safety of others,12 or negligence substantially and appreciably greater than ordinary negligence.13 In some jurisdictions, the term "gross negligence" also encompasses conduct that "smacks of intentional wrongdoing."14
Caution:
Although gross negligence does refer to a different character of conduct than ordinary negligence, one's conduct cannot be grossly negligent without being negligent.15 Accordingly, there is no issue of gross negligence without substantial evidence of serious negligence,16 and if there is insufficient evidence to support a negligence claim, then a claim based on gross negligence must also fail.17 However, evidence of simple negligence alone is not sufficient to establish gross negligence,18 and conversely, some evidence of care does not defeat a gross-negligence finding.19
CUMULATIVE SUPPLEMENT
Cases:
In order to succeed on a claim under Hawai'i law for gross negligence, a party must show that there has been an entire want of care which raises a presumption of conscious indifference to consequences. Smallwood v. NCsoft Corp., 730 F. Supp. 2d 1213 (D. Haw. 2010).
To state a claim for gross negligence under New York law, a plaintiff must establish four elements: (1) the existence of a duty; (2) a breach of that duty; (3) injury as a result thereof; and (4) conduct that evinces a reckless disregard for the rights of others or smacks of intentional wrongdoing. Schwartzco Enterprises LLC v. TMH Management, LLC, 60 F. Supp. 3d 331 (E.D. N.Y. 2014).
To state a claim for gross negligence under New York law, plaintiff must allege four elements: (1) the existence of a duty; (2) a breach of that duty; (3) injury as a result thereof; and (4) conduct that evinces a reckless disregard for the rights of others or smacks of intentional wrongdoing. Alley Sports Bar, LLC v. SimplexGrinnell, LP, 58 F. Supp. 3d 280 (W.D. N.Y. 2014).
"Gross negligence" is defined as the failure to exercise slight care. Doe v. Greenville County School Dist., 375 S.C. 63, 651 S.E.2d 305, 224 Ed. Law Rep. 975 (2007).
"Gross negligence" is a relative term, and means the absence of care that is necessary under the circumstances. Doe v. Greenville County School Dist., 375 S.C. 63, 651 S.E.2d 305, 224 Ed. Law Rep. 975 (2007).