Even though this question already has an accepted answer, I'd like to add mine.
These days, basketball positions are generally defined both by a player's role and their size relative to their four teammates on the court. So out of the five players from a given team currently on the court, the PG is usually the shortest, followed by the SG, then the SF, then the PF, and finally the C is the tallest. That is the reason these positions are often respectively labelled the 1, the 2, the 3, the 4, and the 5: they have an order, and that order is player height.
With that said, the issue of the player's role on the court can overrule their relative height, because positions are of course directly defined by the player's role, while height is just one factor (though arguably the most important factor) that can help players fill that role.
The PF and C positions are similar in requiring size and strength for the purposes of rebounding, blocking shots, and scoring close to the basket. However, traditionally speaking the PF is somewhat shorter, lighter and more athletic than the C, and is therefore more likely to drive (a short distance) past their defender to attempt a shot at the rim, and more dependent on their explosiveness (as opposed to their size) to block shots and grab rebounds. Their lesser height also means it is more important for them to have some shooting ability, since they cannot rely quite as much on dunks, hook shots and layups for scoring. This is why PFs will often flash a nice little midrange jumper; they need one more than a Center does.
As the accepted answer mentions, many of the most successful players in history have achieved that success precisely because they've blended the size of one position with the skills of another. Perhaps the most extreme example of this was Magic Johnson--the tallest, and many argue the best, PG in history. At 6'10", Magic was at least 6-8 inches taller than most players at his position, but he was quick enough on his feet and good enough with his hands to run, dribble, shoot, and (most importantly) pass like a PG. Tall enough to see, pass, or shoot over most of his defenders, but quick enough to drive right past those defenders' taller teammates, Magic was an unstoppable offensive force due to his unique combination of size and skill. Today, LeBron James, being only two inches shorter than Magic was but with much greater athleticism and similar skills, is terrorizing the league using the exact same principles (his superior athleticism offers him an even greater advantage on defense, allowing him to easily guard every position on the court except C).
So how does this all relate to good ol' Timmy? Well, it's as the others have suggested in their answers: Tim Duncan can play the PF and C positions equally well precisely because he has the skills of a PF combined with the size of a C. So which is he? It depends on who else is on the court! When Duncan played with the Admiral, he was always going to be a PF because Robinson was taller, Robinson was already one of the best Cs ever, and Robinson couldn't play PF as well. But after Robinson retired, and whenever he was the biggest guy for his team on the court, Duncan often played the position of Center, and was pretty darn good at it. Furthermore, in today's NBA, where teams are increasingly playing "small-ball", the scenario of PF-turned-C simply by virtue of being his team's biggest player on the court has become even more common. But from what I've read, Duncan has always considered himself a PF first and foremost, so my guess is he's happiest when Tiago Splitter is around to claim the 5.