There are many of Big 3 or any form superstars fusions in the league but most of them just manage to grab some limelight and don't actually deliver the expected performance and chemistry. However, the Spurs Big 3 is definitely one of the most successful combination of stars that went through the test of time.
First, there is no conflicts in the roles within the trio. The corner stone of the team Duncan is the leader of the team, he grab rebounds, the protector under the rim defensively. Offensively, he can be the one to post up in the paint and initiate a play, score himself or feed the sharp shooters on the perimeter, or he can play the supporting cast to set screens and scramble for offensive rebounds. Unselfish and calm he has been playing this role well consistently well for one and a half decade.
Tony Parker who now can be said as the leader of the team and handles the ball most of the time in offense is a explosive and quick point guard, his speed is a threat to most of the teams in the NBA, and with years of experience he has improved his game with his decision in passing. He can drive into the paint and score a floater on his own or feed the ball to the shooters when he is double teamed. With the aging of Duncan, Popovich has molded Parker to be the playmaker and offense initiator of the team.
Manu Ginobili is a very skillful guard who is willing to sacrifice his minutes for the good of his team. He is good in penetrating defense and his drive and layup is so unpredictable and not to mention his euro step, he is also a good perimeter shooter that makes him even harder to guard. Besides skills, he has also big nerves, he can often make big score when he is needed.
Unlike the other stellar teams like Heats, where D Wade's role is actually in conflict with James's, the role to handle the ball and start the plays, which was usually Wade's role in the Heats. When both of them are on the court, Wade can create space for James as he is not good at 3 pointer. I am saying that Wade is not good, but it is obvious that the Heats want James to take the ball. It answers why the better rally better when a bunch of shooters are on court with James.
In San Antonio, now most of the attacks start from Parker or from Duncan posting up and calling for ball in the paint, with smooth ball circulation they find the best open man to make the shot. But if both Duncan or Parker are encumbered by the opponents Manu Ginobili can be a third playmaker to bring some impact on the team, he has the characteristic and ability to handle that. In the normal offense system, he can be a static perimeter shooter who can create space for Parker and others.