When a defendant is acquitted, it means the prosecution did not convince a judge or jury of a defendant's guilt. Most often, we hear a defendant is acquitted when a jury enters a verdict of "not guilty." Acquittals can occur in a few other ways, as well. Whether a case "ends" with an acquittal is important because it determines whether or not a prosecutor can appeal or retry the case.
In the U.S. criminal justice system, defendants don't have to prove their innocence. Rather, the government (the prosecutor) must prove a defendant's guilt beyond a reasonable doubt on every element of the charged offense.
A judge or jury can only convict the defendant—find the defendant guilty—when the government meets this burden by presenting sufficient evidence on each and every element of the crime. If the government fails to do so, even on just one element, it hasn't met its burden and the judge or jury must acquit the defendant—that is, they must find the defendant not guilty.
An acquittal can also occur when a judge makes any ruling—such as on a trial motion—that the prosecution's evidence is insufficient to prove a defendant's guilt.
With the above background in mind, let's break down the meanings and differences between guilty and not guilty, acquittal, hung jury, and innocence.
When a defendant goes to trial, a judge or jury will hear all the evidence, deliberate, and decide whether the prosecutor met its burden of proof in the case. That decision—which must be unanimous for a jury—will be a verdict of guilty or not guilty.
A not-guilty verdict from a judge or jury results in an acquittal because the prosecution failed to meet its burden of proving the defendant guilty. An acquittal can also occur in a few other ways, short of a verdict. For instance, after hearing the prosecution's case, a defense attorney may ask the judge to enter a judgment of acquittal based on the argument that the prosecution's evidence was insufficient for a guilty verdict. An acquittal may also come about if the judge sets aside a jury's guilty verdict due to insufficient evidence. In most cases, a prosecutor cannot appeal an acquittal. (The Double Jeopardy Clause in the Constitution bars prosecuting a case more than once.)
A hung jury does not result in an acquittal. If a jury can't decide one way or another that a defendant is guilty or not guilty, the jury is said to be deadlocked or hung, which often leads to a mistrial. Because no conclusion was reached on the facts of the case, the judge can typically allow a retrial in the case of a hung jury.
The criminal justice system doesn't necessarily decide a defendant's innocence. An acquittal or not-guilty verdict means the jury or judge was not convinced of the defendant's guilt. Basically, the prosecution had its one chance to prove the case and didn't. A hung jury means that no decision was reached either way. While we often hear of guilt and innocence in our justice system, it's really guilty or not guilty of the charges presented by the government.
An acquittal will generally mean the end of the case on those charges. In many criminal cases, a defendant will face multiple counts or charges. If acquitted on all the charges, the case is over and the judge must release a defendant who is in custody (sitting in jail pending trial). For the most part, the U.S. Constitution's Double Jeopardy Clause prevents the government from being able to appeal the acquittal or retry the case. If acquitted on only some of the charges, the defendant's case will continue on the remaining charges.