The Gregorian calendar system used by most of the world today can be generally divided into 2 major eras, labeled as CE (Common era, the one we are currently in, formerly and still widely notated as AD an abbreviation of the Latin "Anno Domini" meaning "in the year of the lord, because it starts counting from the supposed birth year of Jesus)

And prior to that it is BCE (Before Common Era, previously and again still widely called BC for "Before Christ," because it was before the birth of Jesus)

There is no year 0, Jesus was (allegedly, I'll touch on this a bit later) born in the year 1, and we kept counting up from there to the current year or 2023 CE (or AD if you prefer)

For years before jesus, we count backwards, so 2023 years ago would be 1 BCE, 2024 years ago would be the year 2 BCE (or BC if you prefer, one year before the common era/before christ) 3023 years ago would be 1000 BCE

There are different calendars used in different cultures, religions, etc. that mark time differently, that may follow, for example, a lunar year (12 full moons, as opposed to a solar year which marks 1 full revolution of the earth around the sun) or may start counting from a different point in time. An example of the would be the Hebrew calendar which is used in the Jewish religion. It's sort of a hybrid of a lunar and solar calendar, so a year using that system is slightly shorter than a solar year, and also starts counting from a point further back in time (3761 BCE is year 1 in the Hebrew calendar, and the current year is 5783, it's used mostly for things like determining when Jewish holidays fall, which is why you may have noticed that Hanukkah is on a different date every year, and they don't really have an official way of counting before that because that would be understood in the Jewish faith to be the date of creation when God created the heavens and the earth, not that manf modern Jews would take that literally)

As for the date of Jesus' birth, most historians would tell you that it most likely wasn't in year 1 of the Gregorian calendar. And we can't really be totally sure of the exact year. No one started using the BC/AD notation until the 6th century and not everyone got onboard with it at once (it didn't really get any widespread use until the 9th century) some monk in read the bible, compared it to some historical records, did some math, and decided Jesus was probably born 500 some years before, and probably missed the mark by a handful of years.

Prior to adopting this system, people would have counted years from various different points in time, and often wouldn't even have a real number for the year, they might have refered to it as being something like "the 10th year of the reign of King such-and-such of whatever kingdom they happened to live in"

At any rate, years and dates are all pretty arbitrary concepts, we're just slapping labels on it for our own convenience.