Literally translated from Latin, pro-hac-vice means 'for this one occasion only.' It is used when a lawyer from another state is allowed to represent a defendant being tried in a state where their license is not normally valid. A lawyer must pass the bar or receive permission from the bar for each state they want to practice within. If a defendant requests an out of state attorney and the attorney has the qualifications to take the case, and would normally within their own state be able to take such a case, an exemption is made on the one case to allow the person to defend their client.
This is also used when a US citizen is arrested and put on trial in a foreign country for an offense committed on foreign soil. The US citizen is usually able to call on an attorney from the US to defend them if they have the financial means to do so. In these situations, it is customary for a local attorney to work alongside the pro hac vice attorney to explain any differences in law which may be present.