I'm not sure this designation means much, if anything. It seems to just be red meat for Trump and his base. The threshold required to designate or re-brand a DOJ inquiry as a "criminal investigation" is apparently quite low, only requiring "reasonable suspicion of criminal activity" (per the NYT article).
For anyone wanting backstory: This, err, "investigation" is at least the third or fourth concerted attempt by the GOP to bring criminal charges against the Deep State bogeyman. I predict that it ends with NO criminal prosecution, but they'll still find technicalities to drag Christopher Wray, John Brennan, and Peter Strozk, etc. into Senate committee hearings (again), where they'll be publicly berated by GOP members for daring to investigate a president who's lawyer just argued that Trump should not only be un-indictable, but also completely immune from literally any kind of investigation. The only point in favor of this (that I can think of) is that it'd free up Trump to do president things, but he has no real agenda that I can discern, save elevating himself above the law. And building a wall, I guess, but that's not going so hot at the moment.
Republicans have suggested the investigation stemmed from a plot by members of the Obama administration and career intelligence officials, in what they call the "deep state," to undermine Trump.
I cannot fathom why this is still a talking point. Comey announced re-opening an investigation into Hill-dawg days before the election, while there was also an unannounced investigation into the Trump campaign. Ya know, the Trump campaign, the one with Paul Manafort, Roger Stone, and Papadopoulos? The one with Don Jr.'s open acceptance of Russian assistance? The "Russia, if you're listening, get her emails, (wait no it was actually Ukraine that hacked her emails!)" campaign? With so many red flags, not opening an investigation into that camp of folks would have been dereliction of duty on behalf of the intelligence community.
UPDATE: A judge has issued a ruling in which the DOJ is ordered to provide the Mueller investigation with the redacted grand jury testimony. The entire ruling absolutely savages Trump and the DOJ. The judge even recaps damaging elements of the Mueller report and recommends avenues of inquiry.
Things have proceeded like so:
1. Mueller ends his investigation, releases the report, and Congress requests access to the underlying supporting (rightfully) classified grand jury info.
2. DOJ initially says "OK, let us get back to you," and then never turns over the material. They then issue statements saying they won't turn over anything, since they don't recognize the legitimacy of the House Judiciary Committee request and overarching investigation.
3. Pelosi formally introduces an impeachment inquiry, which gives the Committee's request enough teeth that this judge rules "WTF, DOJ? Give the Congress what it is legally entitled to within the next three business days."
I've been shocked with the way Barr has headed the DOJ. Flying to Italy for meetings in which he chases down Trumpian conspiracies totally contradictory to Mueller's report (which was issued by the DOJ earlier this year!). How has he not been forced to recuse himself from any effort to investigate Ukraine? Trump mentioned to Zelensky that Barr would work with Giuliani so that Ukraine could investigate the Bidens and the 2016 election, the whistleblower reports the phone call to Congress, and then Barr's DOJ unsuccessfully attempted to withhold the report from Congress. Barr should be impeached too. The New York City Bar association (single "r", guys!) has basically said as much.