The head on the front and the statue on the back of this denarius both depict Augustus, the first emperor of Rome. However, the coin was minted in Rome before he took the imperial title Augustus, when he still was known by his birth-name, Octavian.
On this coin, Octavian's head resembles that of a classical sculpture of the Greek god Apollo. In addition, he wears a laurel wreath, an honor that the Roman Senate bestowed in 36 B.C. to celebrate his defeat of Sextus Pompey in a naval battle. Very likely the image on the back refers to this event too, for the Senate had also voted to erect a victory monument, with Octavian's statue standing on a column decorated with the prows of the vanquished ships.
The Latin inscription IMP CAESAR stands for "Imperator Caesar." It refers to the military title, Imperator, meaning "victorious general," that the Senate conferred on Octavian. Octavian used this title together with his name, Caesar; which he inherited from his adoptive father, Julius Caesar. The date when Octavian received the title Imperator is uncertain.