A hung jury is when the jurors in a trial can not agree on a verdict after hearing all the evidence and discussing, or deliberating, the facts of the case. This can occur for a variety of reasons, but it usually involves differences of opinion that can't be resolved after lengthy periods of deliberation. When the jury is unable to agree on a verdict, in some jurisdictions the judge may discuss the matter with them, and request that the jurors reconsider their positions. A jury that still can't reach a consensus is called a hung jury, which usually means that the case will be tried again with a new jury.
At a trial by jury, the jurors are responsible for rendering the verdict in the case, i.e., guilty or innocent in a criminal case or liable or not liable in a civil case. The jury listens to the entire proceedings, hears all the testimony, and sees all the evidence that is submitted while the case is being tried. After the closing arguments, the jury begins a process called deliberation. While they are in deliberation, jurors are alone with one another in a private room discussing the disposition of the case. They have access to transcripts of the testimony, and any evidence is available for their review.
In general, jurors are able to take as much time as they need for deliberation. The goal is for them to be united on a verdict, but at times this does not happen, and the jury becomes deadlocked, or unable to agree. A deadlocked jury is unable to reach a decision either way. In some countries, the jury needs to be in unanimous agreement to render a verdict in a criminal case, but in other countries a majority agreement suffices. For example, in some countries 10 out of 12 jurors are enough to render a criminal conviction.
A deadlocked or divided jury is a hung jury. In order to try to prevent this, in some jurisdictions the judge is allowed to discuss the situation with the jurors and ask those who are in the minority, i.e., the holdouts, to reconsider their position. In the U.S., this is called an "Allen charge." The judge typically reminds the jury of the importance of reaching a conclusion in the trial and how much time and effort has already been expended.
When there is a hung jury, in most parts of the world it can mean the case will be tried again with a different group of jurors which creates added expense. In the U.S., this is called a mistrial. In the criminal system, the prosecution can decide to let a case be dismissed or pursue a retrial. If there is a strong case, the prosecutor usually seeks a new trial with a fresh jury.