Hung jury is a colloquialism for a situation in which the jury cannot meet the requirements to render a verdict. “Not guilty” verdicts don’t come about because the entirety of the jury is unconvinced of guilt, instead they come about because the jury collectively agrees that the prosecution has not proven their case to the burden of proof required and has rendered a verdict.
In a hung jury the jury hasn’t rendered a verdict, so the original jeopardy never concludes, it continues on. The case is ruled a mistrial and can be brought again by the prosecutor. (Some mistrials can be dismissed with prejudice, and they cannot be retried, but that usually involves the prosecutor acting in a malfeasant or inappropriate way.)
Since it’s GQ and it’s a weird thing not many people know, it’s worth mentioning the requirement that guilty verdicts be unanimous is not universal.
In the United States, both Louisiana and Oregon do not require the jury to be unanimous to render a verdict in a criminal trial. In Oregon a unanimous jury is required to convict for murder, in Louisiana if 10 out of 12 jurors agree, that’s enough to sustain a murder conviction.
Military courts-martial also do not require unanimous verdicts universally. If the crime carries a mandatory death sentence, then the courts-martial panels members must rule unanimously. For lesser crimes there requirement is less, for a crime that carries a mandatory life sentence it only requires 3/4ths of the courts martial panel to agree. Other crimes require concurrence of 2/3rds of the courts-martial. The military justice system has several features that would be incompatible with the constitutional provisions for conducting trials (this is because of essentially the concept that under the constitution Congress can spell out a special process for adjudicating crimes under the guise of military discipline), for example the convening authority in a courts-martial (the officer who is bringing charges), personally selects the members of the courts-martial. This goes against the typical concepts we see in civilian court jury selections. While there are peremptory challenges in the military justice system, there is only one allowed. Additionally strictly speaking many courts-martial trials do not have a panel (jury) that is made up of “a jury of peers.” If an officer is being tried it is required that all members of the panel be officers. If a warrant officer is being tried, the panel can be composed of a mixture of officers and warrant officers (it could still be all officers), if an enlisted person is on trial they can request enlisted members be on the panel, but even then the convening authority is only required to make 1/3rd of the panel enlisted, so you have a case where there will be people who are not “peers” of the accused rendering judgment of them.