Is it when the domain name was first registered or when the site is fully completed? I'm thinking that it's the former....but you never know with Google.

Maybe an algorithm of bot? Maybe the date of the first ARTICLE on that site?
You never know with Google, that's true, I doupt it's something SIMPLE so we can crack it easily.

Age is considered by the registering date, in this case will be the domain whois data.

My guess is from the very first time Google indexed the site's content.

I'd imagine it's a compilation of several factors, including (but not limited to):
First domain registration
Secondary/Tertiary registration
Date of first upload/post to site
Time elapse between the above 3

I suppose we may never know, but this makes sense in my mind.

Pretty sure they have a Magic 8 Ball algorithm which determines many factors. I'm sure domain age could be one of them. Why don't you ask Matt Cutts?

Only one way: The date it was first registered. That's when the domain was born.

Originally Posted by TrevorB

Only one way: The date it was first registered. That's when the domain was born.

Don't be too sure, how about re-using an old domain with a new website. Which "date" of creation would you take in consideration?

I'm not sure about google, but I've seen other ranking sites use web archive.
For example, I bought a domain that's 17 years old. The first thing I did was put a tag in my htaccess so that the waybackmachine would kill all the old archive versions of my domain. Now my domain shows are 0yrs old on some sites and 17yrs old on others.