Jury tampering is the criminal act of trying to persuade a juror's or jurors' vote about a trial through means other than evidence presented in court.
Jury tampering is often attempted by offering bribes, using intimidation, or having certain people speak with the juror to try to convince them to vote in a certain way.
The reason why jury tampering can be such an issue is because it can make the results of the trial artificial. In other words, jury tampering destroys the legitimacy of the trial. For example, if a juror is bribed $20,000 to vote "not guilty" in an armed robbery case, then their vote is illegitimate.
People who are caught participating in jury tampering can be prosecuted and sentenced to a punishment if they are found guilty.