Augustus (pl. Augusti) is Latin for "majestic" or "venerable". It is chiefly significant as a cognomen first awarded to Gaius Iulius Caesar Octavianus (who styled himself "Imperator Caesar" on January 16, 27 BC, along with the office of princeps senatus (lit., "prince of the senate"), the parliamentary leader of the house. Caesar Augustus continued to be elected consul each year until 23 BC. He was given imperium maius (his supreme command outranked that of any provincial governor), and owned all of Aegyptus as private property (he had succeeded Cleopatra VII of Egypt as Pharaoh in 30 BC).
In 23 BC, in the so-called "Second Settlement", the Senate voted him tribunicia potestas ("tribunician power"), thereby investing him with the powers of a tribune of the people, most importantly personal inviolability (sacrosanctitas) and the right to veto any act or proposal of any magistrate (ius intercessio). His power was further augmented in 19 BC when he accepted an ad personam grant of consular imperium (i.e., without holding the consulate itself) and in 18 BC when he was elected Pontifex Maximus.
Augustus subsequently became the principal rank associated with the Roman Emperors; a designated successor to an emperor adopted the title Caesar (later Nobilissimus Caesar, "Most Noble Caesar"), or would occasionally be awarded the title Princeps Iuventutis ("Prince of Youth"), and adopted the titles "Imperator" and Augustus upon accession to the full imperial dignity; a wife or mother of the emperor could be invested with the title Augusta. In this sense, "Augustus" is broadly comparable to "Emperor", though a modern reader should be careful not to project onto the ancients a modern, monarchical understanding of "emperor"; there was no constitutional office associated with the imperial dignity. The emperor's personal authority (dignitas) and influence (auctoritas) derived from his position as princeps senatus, and his legal authority derived from his consulari imperium and tribunicia potestas; it is more accurate to describe the emperor as "princeps senatus et pontifex maximus consulari imperio et tribuniciae potestate" (loosely, "Leader of the House and Chief Priest with Consular Imperium and Tribunician Power").
In many ways, Augustus is comparable to the British dignity of prince; it is a personal title, dignity, or attribute rather than a title of nobility such as duke or king. The emperor was most commonly referred to as princeps (basileys, "king", in Greek). Later, under the Tetrarchy, the rank of Augustus referred to the senior emperor, while Caesar referred to the junior sub-emperor. The three principle titles of the emperors -- Imperator, Caesar, and Augustus -- were rendered as autokratôr, kaisar, and augustos (or sebastos) in Greek. The Latin title of the so-called "Holy Roman Emperors" was usually "Imperator Augustus" ("August Emperor"), which conveys the modern understanding of "emperor" rather than the original Roman sense (i.e., the "first citizen" of the Republic).
As a note of historical interest, the first modern use of the original sense of "emperor" was in the French Republic (République française). Napoléon Bonaparte, who was already First Consul of the French Republic (Premier Consul de la République française) for life, was crowned "Emperor of the French (Empereur des Français) in 1804; despite being ruled by an emperor, it continued to be the French Republic until 1808, when it was renamed the French Empire (Empire français).