Absolutely nothing. You need to have a starting point, and for historical reasons we ended up with that one. It isn't a meaningful date for anybody, but it turns out having a common reference point is more important than having a significant reference point, so nobody cares.
It's actually a very meaningful date to a lot of people on this planet, although I'm not one of them.
We used to refer to years past that date using a short phrase in a dead language. However, this short phrase in a dead language referred to a religious figure, which is Not OK. So we decided we'd rename it "Common Era" but keep the numbers the same because that would be a big hassle. As a result, our calendar still counts how many years have passed since the alleged birth of Christ, but because people might be offended by the words "Anno Domini" we've called it something different.
If I were in the position to pick a new calendar start date, I'd probably just go with the Unix Epoch... AE, Anno Epocha? We'd now be in the year 46AE :)
As galdosdi surmised, it's not about whether you're not a believer, it's about that 1 AD isn't believed to be the date for Jesus's birth. At some point historians & theologians realized the calendar was incorrect, and so they had a choice: keep the reference point everyone was familiar with, even if that date is no longer significant, or switch to a better estimate for Jesus's birth, keeping the calendar significant. People decided that commonly known was more important than significant, and so we're left with a BC / AD split, where the reference point is longer meaningful.
While the modern estimate certainly has uncertainty too (how could we ever _know_ such a thing with complete certainty?), there's no way it's _less_ accurate than the original estimate made by some random monk in the middle ages, working with much less data. It does not make sense to privilege that random monk's guesses over today's guesses.
According to Wikipedia, there's two different methods -- written Roman records of Herod as mcphage mentions, or using written Roman records of Pilate's crucifixion and subtracting the claimed age of Jesus at that time. Both methods give years that are in the same ballpark, roughly 4 to 6 BC, which should give confidence that they are close. No method gives an answer of around 1 AD. (Actually, it's pretty impressive that some monks working hundreds of years later in the dark ages are no more than a few years off from today's best estimates)
Anyway, this assumes historicity of the accounts saying he was born during the reign of Herod but that's kind of complicated by the Moses imagery; this isn't exactly neutral and unimportant. But I guess that is as good a basis as any to try and determine the real date.