Your 'crib' is your home, the term has made its way over to the UK from the US, MTV have a show called 'Cribs', which is well known (debateable) people showing all of us mere mortals their homes, which are riduculously large and ridiculously decorated.
That's what the line of the song is talking about wanting a brand new house in an episode of Cribs.
Sorry, I got a little 'b' happy in my first response. :o)