OK, I warn you I lecture on this stuff. Report and have this deleted if I get carried away (as I did on the sexism post) 
It isn't unreasonable to think of personality as having two main types fof traits: innate and acquired.
Nature: It has long been believed innate characteristics are really strong. Things like temper, competitiveness, active traits are there from birth. But the Human Genome programme (completed in 2000) couldn't find a gene that connected to Big 5 personality traits (Openess, conscientiousness, extravertism, agreeableness and neuroticism). Don't get taken in my newspaper claims of them finding a criminal gene, they didn't!
But that is directly opposed to the many twin based studies which have found similarities in personality traits in twins - however the majority of twin studies were with twins who were usually brought up in the same household, where it is not unusual to treat identical twins as one entity in two bodies!
I suspect that the Big 5 are our basic tendencies for beahviour.
Nurture: social learning theory and it like have been around for decades and do seem to explain how learned behaviour affects our personalities. We can copy what we see and become carbon copies of our parents. Or dislike their personalities so much we become polar opposites - or anything in between, depending on the personalities of those parents and what they themselves may be conforming to / rebelling against.
Think: am I my mother??
In my case my mum has a horror of becoming her mother. She asked us to tell her if she started to show such traits. She did. We did. She acted wholly within character and didn't speak to us for months!
Think: national characteristics. Where do national stereotypes come from?
So, given all of that - I'm firmly in the humanist camp. We are born with innate characteristics (basic tendencies) that our upbringing modifies and moulds according to where we are, who we are with and who we see as role models. Media, music, parents, teachers, friends and the general social milieu all act upon any innate characteristics we may have been born with. And don't forget personal choice!
We live through a dynamic process that changes the Big 5, jobs, loves, life etc, and we can be somewhat different at different stages of life.
Or should I have just said it is a mix of both?