Our current calendar system (BC/AD) was invented by a sixth-century
Christian monk named Dionysius Exiguus.  He calculated the date of Jesus's
birth and proposed expressing dates as years before or after that time. 
The system was first used by Dionysius' friend Cassidorus, a learned monk
writing in the year 562.  It came into common use in the eighth century. 
<p>

This system was adopted before cultures around the Mediterranean had
borrowed the concept of "zero".  Therefore, there is no year 0 in the
BC/AD system.<p>

Because the system is explicitly Christian (AD stands for Anno Domini,
"In the year of our Lord"), some people have begun using the terms CE
(Common Era or Christian Era) and BCE (Before the Common Era) instead. 
The new terms function in exactly the same way, except that one normally
writes both CE and BCE <em>after</em> the date.  (In correct usage, the
term AD appears <em>before</em> the year, as in "AD 1998"). <p>

Before the time of Dionysius Exiguus, Christians and others used other
systems of dating.  Common systems included dating by the regnal year of a
local king or by a tax period in Egypt or from the (presumed) foundation
of Rome or from the beginning of the Seleucid empire or by Olympics. 
<p>

It turns out that Dionysius's system was probably in error by a few years.