Officers of the Praetorian Guard stab the emperor Caligula at the Palatine games. The guards make his uncle Claudius emperor.
Respecting what followed, two different accounts are given. Some say, that, whilst he was speaking to the boys, Chaerea came behind him, and gave him a heavy blow on the neck with his sword
Some of the plotters may have hoped to restore the Republic, and Caligula's death marked the official end of the Julii Caesares in the male line.
Based on Wikipedia: Caligula
At least some of the conspirators might have planned this as an opportunity to restore the Roman Republic and aristocratic privileges.
Caligula's death marked the official end of the Julii Caesares in the male line, though the Julio-Claudian dynasty continued to rule until the demise of Caligula's nephew, the Emperor Nero.