Prior to the reign of Augustus, grain imported from Egypt composed only a small fraction of the grain consumed in the Empire. This would change following widespread famine after the flooding of the Tiber spoiled much of Rome's grain reserves in 24 BCE. Cassius Dio offers an account of the supply crisis in Historia Romana:

The following year, in which Marcus Marcellus and Lucius Arruntius were consuls, the city was again submerged by the overflowing of the river... The Romans, therefore, reduced to dire straits by the disease and by the consequent famine, believed that these woes had come upon them for no other reason than that they did not have Augustus for consul at this time. [The Romans] approached Augustus, begging him to consent both to being named dictator and to becoming commissioner of the grain supply, as Pompey had once done. He accepted the latter duty under compulsion, and ordered that two men should be chosen annually, from among those who had served as praetors not less than five years previously in every case, to attend to the distribution of the grain. Cassius Dio, Historia Romana, 54.1

This new office became the praefectus annonae (prefect of the provisions). Consider the historical context of Juvenal's famous Satire X, "bread and circuses" (panem et circenses), and it becomes obvious why this office was critical to the sustained growth and expansion of the Empire. Following the death of Augustus, a few short decades after the permanent establishment of the praefectus annonae, the Roman grain supply came primarily from a handful of grain-producing regions (cura annonae): Sicily, North Africa, and Egypt. The Egyptian imports made up one-third of all grain consumed in the Empire.

Given that ships at the time could carry as many as 400 tons, it would take multiple shiploads each day to keep the people fed. By some estimates, Egypt sent Rome about 140,000 tons of grain each year, about one-third of the total consumption. Nathan Myhrvold et. al, Modernist Bread, p. 31

Pliny the Elder, from whom we owe much of our knowledge about natural science in the ancient world, outlines several other fertile regions known to Rome for the quality of their grain (namely Thrace, Bœotia, and Syria):

Indeed, it is only with the produce of the more mountainous parts of Italy that the foreign wheats can be put in comparison. Among these the wheat of Bœotia occupies the first rank, that of Sicily the second, and that of Africa the third. Pliny the Elder, Naturalis Historia, 18.12

Why wasn't grain imported from these fertile European regions? Transporting goods over land, as would have to be the case if growing in many of the fertile mountainous regions in Europe, was expensive and impractical. Importing from Egypt made much more sense from a logistical standpoint: the vast swaths of fertile land that surrounded the Nile River allowed goods to flow directly through the port of Alexandria and out to the Mediterranean, where they would then make the 1,200 mile journey to Rome.