To propagate and continue the human race. 

We are biological programmed to have "lust" which have one single big result. Children. Only Dolphins and monkeys also have sex because of lust. Rest is purely surival instinct, which we humans also have a bit. 

Depends on your beliefs, really. I do not think their is a correct answer here. Some may say to continue on the human race and another may question that statement with "why should the human race continue on?" Is there a bigger picture here?
Why are we able to ask ourselves these questions when a dog or cat is not yet we still have the same reproductive functionality of both. 
I would say ask yourself what you think your purpose is here, maybe it is something like taking care of your child, being a florist or space travel. Whatever you believe your purpose to be is probably why you were born. 
Unless of course one day the sky opens up and some guy looks down at his project and tells us we are all part of his sons middle school biome science project. 

When we are born we do not have anything but we die with our name. We are born so that we can write our name in the pages of history. Future generations can remember us for our good works. We have to make great efforts to realize our birth.