In the universe of "The Smurfs" Papa Smurf is the absolute leader. His main duties are to ensure that all the smurfs live in harmony and he makes the important decisions in the name of smurfkind.
Papa Smurf is traditionally said to be 542 years old, while all the other Smurfs (save Grandpa Smurf) are said to be a little over 100. I can't remember them ever explaining why there were only two old smurfs, but then there are a lot of unexplained things going on in that world.
It is well known that Papa Smurf is a powerful mage. He lives in a laboratory where he can create chemical and magical potions and objects. He likes to try to solve existant and imaginary problems using his potions. He is often successful, but sometimes his magic backfires terribly. Such as the times he made a chemical that turned people into scary monsters, or the incident where he created an entire village of evil smurfs.
You can easily spot Papa Smurf in a crowd because he has a white beard and wears red clothing. Of course I am sure you already knew that all the other smurfs wear white and are smooth skinned. When Papa speaks it is without substituting the word smurf into every sentence. This ensures that other creatures can actually understand his speech. His speech and diplomacy are really what sets his personality apart from the other smurfs. But from time to time even Papa Smurf will lose his cool. This usually happens when all the smurfs are travelling, and smurf after smurf will ask him if it is much further. He will usually calmly respond that it isn't much further. He will do this until the third time they ask, at which point he will get annoyed and say that "Yes, it is much further".