The Roman office of tribune of the people (tribunus plebis) was established in 494 BC, about 15 years after the foundation of the Roman Republic in 509. The plebeians of Rome seceded as a group -- that is, they left the city entirely -- until the patricians agreed to the establishment of an office that would have sacrosanctity (sacrosanctitas) -- that is, the right to be legally protected from any physical harm -- and the right of help (ius auxiliandi) -- that is, the right to rescue any plebeian from the hands of a patrician magistrate. Later, the tribunes acquired a far more formidable power, the right of intercession (ius intercessio) -- that is, the right to veto any act or proposal of any magistrate, including another tribune of the people ("veto" is Latin for "I forbid"). The tribune also had the power to exercise capital punishment against any person who interfered in the performance of his duties (the favourite threat of the tribune was therefore to have someone thrown from the Tarpeian Rock). The tribune's sacrosanctity was enforced by a solemn pledge of the plebeians to kill any person who harmed a tribune during his term of office. In about 450 the number of tribunes was raised to ten.
Tribunes were required to be plebeians, and until 421 this was the only office open to them. In the late Republic the patrician politician Clodius arranged for his adoption by a plebeian branch of his family, and successfully ran for the tribunate.
By extension from the technical Roman governmental usage, some modern politicians have been identified as "Tribunes of the People."
Throughout the Republic and its fall, certain powerful individuals used the tribunes for their personal glory and gain. Clodius and Milo were both tribunes who used violence in the courts and government in order to achieve the needs and requests of Pompey and Caesar. Further more, when the Senate refused to grant Caesar all his requests he turned to the tribunes to grant him all he wanted -- ie. Pompey's veterans lands and him a further governship of Gaul. Again violence was used against those tribunes that prevented their quest for glory.
Because it was legally impossible for a patrician to be a tribune of the people, the first Roman "emperor", Caesar Augustus, was offered instead all of the powers of the tribunate without actually holding the office (tribunicia potestas or 'Tribunician Power'). This formed one of the two main constitutional basis of Augustus' authority (the other was imperium proconsulare maius). It gave him the absolute right of veto and the authority to convene the Senate. Also, he was sacrosanct, had ius intercessio, and could exercise capital punishment in the course of the performance of his duties.
Most emperors' reigns were dated by their assumption of tribunicia potestas, though some emperors, such as Tiberius, Titus, Trajan, Marcus Aurelius, etc, had already received it during their predecessor's reign. Also, Marcus Agrippa and Drusus II, though never emperors, received tribunicia potestas.