PIRA is the abbreviation for the Provisional IRA, the main (ex-)terrorist organization in Northern Ireland. It is normally called the IRA, but that term also refers to the fighters for independence in the early 20th century and the subsequent civil war in the Irish Free State, as well as to several other groups who have claimed the mantle of the original IRA.
Serious people like the Army and MI5 always refer to the IRA as PIRA, to make clear which group they mean. On army bases, the semi-humorous posters exhorting vigilance call them PIRA. The distinction is no doubt more important to them because of the groups' histories.
The militant wing of the IRA (the Provos) split from the IRA (the 'Official IRA') in 1969 and declared a Provisional Army Council, which is where they get their name. They committed the vast majority of republican terrorism until 1997, when they and their political wing Sinn Féin committed to a ceasefire. Thereupon several rejectionist groups split off from them, such as the Real IRA.