In criminal matters, this can involve both rendering a verdict and determining the appropriate sentence. In civil cases, the decision is whether to agree with the plaintiff or the defendent and the amount and nature of the results of the trial.
Typically, a jury must come to a unanimous decision before delivering a verdict, however there are exceptions. When a unanimous decision is not reached and the jury feels that one is not possible, they declare themselves a 'hung jury' and the trial will have to be redone at the discretion of the parties involved.
The best known dramatization of this legal process is the film, 12 Angry Men