Missing-nin (抜け忍, nukenin, English TV: Rogue Ninja, Literally meaning: runaway shinobi) are ninja who abandon their village with no intention of returning. Missing-nin are criminals in effect, if not before their defection then certainly after abandoning their duties. As such, missing-nin are listed in their village's Bingo Book to be killed on-sight; Kirigakure's hunter-nin are specifically assigned to eliminate these missing-nin. Although some missing-nin may continue wearing their village's forehead protector, they no longer swear allegiance to their village; members of Akatsuki - all of them missing-nin - carve scratches across their forehead protectors to symbolize they have rejected their village.
Leaving the village does not necessarily automatically make one a missing-nin. Tsunade withdraws from life as a ninja and departs from Konoha following the Second Shinobi World War, but she is at no time considered a missing-nin by the village. Jiraiya informs her, however, that if she aids Orochimaru - an enemy of Konoha - that her status will change and he will be forced to kill her.
Likewise, being branded a missing-nin does not guarantee their former village will seek them out as a criminal. Itachi Uchiha becomes a missing-nin after the Uchiha Clan Downfall, but he does so under orders of Konoha's leadership; while most of Konoha's population does indeed consider Itachi a criminal and treats him as such, its leaders are privately aware that he remains loyal to Konoha. Similarly, when Sasuke Uchiha defects from Konoha and becomes a missing-nin, the Fifth Hokage decides not to pursue him as a criminal as a favour to Naruto Uzumaki. The Sixth Hokage Candidate later withdraws this leniency and orders his execution. For his help during the Fourth Shinobi World War and the good word of the Sixth Hokage, Sasuke is ultimately pardoned for his crimes.