At the time when this web page was written, the current year in the Hebrew calendar is 5763 (2003 in the Gregorian or Christian calendar). The big question is (drum roll please!): what is the origin of the numbering of years in the Hebrew calendar? The answer is that the year number in the Hebrew calendar represents in the number of years since the beginning of the Creation of the world (Genesis 1:1). This number is determined by adding up the ages of people in the Hebrew Bible since Creation. More specifically, the birth of Adam on the 6th day of Creation is the actual starting point for counting the years in the Hebrew calendar. At first glance, given the year 5763, this would mean that the world began in 3760 B.C.E. in the Christian calendar (3760 + 2003 = 5763), and that this was Year 1 in the Hebrew calendar. However, the meaning of what a "day" is in the Hebrew bible is not what we think a day means in the sense of a 24-hour day. Even the concept of a "day" in the seven days of creation does not represent a 24-hour day according to Orthodox Jews since they point out that the Sun did not appear until the 4th "day". Until the 4th "day", they reason, the idea of a 24-hour "day" would be meaningless. Therefore, the Hebrew year number is not necessarily supposed to represent a scientific fact.
http://www.angelfire.com/pa2/passover/jewishcalendar.html
2.13 How does one count years?
In about AD 523, the papal chancellor, Bonifatius, asked a monk by the name of Dionysius Exiguus to devise a way to implement the rules from the Nicean council (the so-called ``Alexandrine Rules'') for general use.
Dionysius Exiguus (in English known as Denis the Little) was a monk from Scythia, he was a canon in the Roman curia, and his assignment was to prepare calculations of the dates of Easter. At that time it was customary to count years since the reign of emperor Diocletian; but in his calculations Dionysius chose to number the years since the birth of Christ, rather than honour the persecutor Diocletian.
Dionysius (wrongly) fixed Jesus' birth with respect to Diocletian's reign in such a manner that it falls on 25 December 753 AUC (ab urbe condita, i.e. since the founding of Rome), thus making the current era start with AD 1 on 1 January 754 AUC.
How Dionysius established the year of Christ's birth is not known (see section 2.13.1 for a couple of theories). Jesus was born under the reign of king Herod the Great, who died in 750 AUC, which means that Jesus could have been born no later than that year. Dionysius' calculations were disputed at a very early stage.
When people started dating years before 754 AUC using the term ``Before Christ'', they let the year 1 BC immediately precede AD 1 with no intervening year zero.
Note, however, that astronomers frequently use another way of numbering the years BC. Instead of 1 BC they use 0, instead of 2 BC they use -1, instead of 3 BC they use -2, etc.
See also section 2.13.2.
It is frequently claimed that it was the venerable Bede (673-735) who introduced BC dating. Although Bede seems to have used the term on at least one occasion, it is generally believed that BC dates were not used until the middle of the 17th century.
In this section I have used AD 1 = 754 AUC. This is the most likely equivalence between the two systems. However, some authorities state that AD 1 = 753 AUC or 755 AUC. This confusion is not a modern one, it appears that even the Romans were in some doubt about how to count the years since the founding of Rome.
http://www.tondering.dk/claus/cal/node3.html