I wrote some of this in another thread but I always feel empathy for a person making an ELI5 request -- I've done so myself! -- so this is the Cliff Notes version:
This deposition was taken by a right-leaning nonprofit organization called "Judicial Watch." Judicial Watch filed a Freedom of Information Act ("FOIA") request with the State Department because it wanted more information about how it was that Clinton's close aide, Huma Abedin, came to "double dip" as a "special government employee" while simultaneously working for the State Department.
The State Department said it didn't have any such email communications and Judicial Watch believed them until it came out that all Clinton's email communications -- business and personal -- were done via @clintonemail.com and that that was why the State Department didn't have any emails regarding Huma's service at the State Department; if they existed, Clinton had them comingled with her personal email on the server in her bathroom.
Ultimately, Clinton & Co. culled through the personal and business emails and provided the State Department with the ones they thought were business related and deleted the rest. (But apparently copies of some, if not all, of the deleted emails still exist because, unbeknownst to Clinton & Co., the Denver-based company handling the server was backing them up in the cloud. In addition, some of the deleted emails may also be obtainable from the person at the other end of the conversation or someone copied in it; see the reference to the Petraeus emails -- which Clinton & Co. apparently didn't provide to State despite the fact that they were clearly business related -- in the OIG report leaked to the press earlier this week.)
Judicial Watch, not surprisingly, now finds it difficult to believe anything the State Department says about Clinton's email communications while she was Secretary of State, and the judge in the case has questioned, citing Supreme Court precedent, whether the State Department and Mrs. Clinton “purposefully routed…document[s] out of agency possession in order to circumvent a FOIA request.”
As a result, the judge is allowing Judicial Watch to get more testimony from