Short answers, pulled from the story.
The Donations of Alexandria were a political ceremony conducted by Mark Antony and Cleopatra VII in autumn 34 BC. Territories and royal titles were distributed to Cleopatra's children, with Caesarion receiving the greatest recognition as King of Kings, King of Egypt, and legitimate heir to Julius Caesar.
The Donations of Alexandria took place in autumn 34 BC, in the gymnasium of Alexandria. A similar ceremony had been held two years earlier at Antioch in 36 BC, with Octavian's full approval.
Alexander Helios received Armenia, Media and Parthia; his twin sister Cleopatra Selene II received Cyrenaica and Libya; and their younger brother Ptolemy Philadelphus was awarded Syria, Phoenicia and Cilicia. Cleopatra VII was proclaimed Queen of Kings and confirmed as ruler of Egypt, Cyprus, Libya and central Syria.
Caesarion was proclaimed King of Kings and King of Egypt at the Donations of Alexandria. He was also named the son of the deified Julius Caesar and declared the legitimate heir to Caesar's name and legacy.
Rome's Senate refused to approve the Donations of Alexandria, and the recognition of Caesarion as Julius Caesar's legitimate heir directly threatened Octavian's authority. Octavian's power rested on Caesar's adoption of him, documented in Caesar's will, which had given him popularity and the loyalty of the Roman legions.
The Second Triumvirate expired on the last day of 33 BC and was not renewed following the Donations of Alexandria. Octavian's escalating conflict with Antony led to the final war of the Roman Republic, which Octavian won, inaugurating the Imperial era.