I was not baptized until I was 35 (I'm 44 now). I went to Mass regularly with my paternal grandfather when I was a child, but my mother (who is an atheist) never wanted me baptized. For some reason, when I hit my mid 30's I felt drawn back to Mass. I started going every Sunday but was unable to participate fully. Finally it was my desire to receive Holy Communion - FINALLY, for the first time in my life, that drew me to being baptized.
So it was not baptism itself that I was drawn to, it was that I knew I had to do this to gain access to all the sacraments of the Church.
And please also consider that the parish I was at during this time was probably one of the WORST I could have possibly been going to for catechesis. It is amazing that I've stayed and become a Faithful Catholic after the experience -- so when it comes to understanding the salvific aspect of baptism, I don't think we ever were told anything about it that I can remember.
It was a kum-bye-ya sorta place.