Do Birthdays make one older?

So, I`m a year older ! No I`m not!
I`m a day older than I was yesterday, and by the time I finish writing this I`ll be ten minutes older than I was when I started writing it. So why do we say at birthdays that one is a year older? Thinking about that set me pondering - when were birthdays first thought of? Did they mark or celebrate them in the first century AD, or in Roman times, or was it even earlier than that, I read in the bible accounts of meals and feasts, were any of these perhaps birthday celebrations?? Or when did somone first decide to do it, and who was the first person to celebrate a birthday?!