In the United States, the term of office for federal judges is life during "good behavior." In other words, a federal judge, once approved by the Senate, can stay on the bench until he or she dies or decides to retire. The only exception to this rule is that judges can be impeached for "high crimes or misdemeanors." This is very, very rare.
The reasoning behind this term is that judges need life terms in order to be independent. If they could be easily removed by Congress or the President, they would tend to rule in ways that those people wanted. This would mean that they would not truly be a check/balance the way they are supposed to be.
The term of office for federal judges is unlimited. Unlike members of Congress or the President and the Vice President, there is no set number of years for a judge once he or she assumes the position. They are able to hold their position for life unless they are impeached for breaking the law or other impeachable actions. They also could give up their position by retiring or resigning.
According to the Constitution, the President appoints federal judges. To be sure the President appoints good judges, there is a check on his power to make these appointments. That check on his power is that the United States Senate must confirm the appointment made by the President. This is why the confirmation process for the judges must be very thorough and detailed. Once a judge is confirmed, that person could remain in the position for many, many years. Unlike Congress or the President and the Vice President, federal judges are not elected. This frees these judges from any political pressure when deciding a case.