The meaning of domain age is the length of time since the domain name has been registered.
The domain age starts from the day or minute you register the domain.
The older the domain is in years the more ranking power it has as Google and Yahoo, Bing etc all take the domains age into consideration when deciding where to rank your websites pages.
Usually for the first 6 months of a domains age and website age the website will not rank as good until the 6 months has passed.
The search engines want to ensure the website is around to stay.
Then once you have the website online for 6 months or longer and you continue updating the website with fresh and new content then the search engines will start ranking your content higher up.
A new domain can rank good but the older the domain the more ranking power it has.
Older domains and websites are trusted more than newer websites and domains.