Social security/Número de Seguridad Social (Madrid)

Hi there,
Living in Madrid for two months now and have all the paper work done. I also got a document "asignacíon de número de seguridad social o número de afiliacón". Doe anybody know if this social security number means that I have insurrance (and can go to a doctor)? And apparently you can also add family members? Does anybody have experience with this? The Spanish websites are not so clear.
Thanks, Jitske