How do we explain defying gravity by objects on the wall of a rotating drum? 
Image courtesy: The calculus story: A mathematical adventure; David Acheson
How is the static friction balancing the gravity which seems to be provided by the normal force of wall on people. 
I understand that centripetal acceleration (providing normal force and hence friction) has to be provided by a net force in centripetal direction. However, in this problem, what is providing this force. 
 A: 
I understand that centripetal acceleration (providing normal force and hence friction) has to be provided by a net force in centripetal direction. However, in this problem, what is providing this force. 

Is a force caused by an acceleration? Rather think oppositely: We see acceleration happening around us in this World so we raise the question of what causes such acceleration. This "cause" is then called a force (and follows Newton's 2nd law). So, acceleration is caused by a force. The centripetal acceleration here is caused by the normal force. Not the other way around.
Now, how can this be...
Imagine driving fast and suddenly turning your car. Your body "wants" to continue forward (due to its inertia), but the car is now moving sideways. It thus pushes you with it.
In other words, the car moves into you. This is where the normal force appears. This normal force causes you to move along with the car, i.e. it gives you an acceleration sideways. (Were the car not able to exert a big enough normal force to cause your necessary acceleration, then you would be breaking through the side of the car.)
In the rotating drum in your picture, the wall is constantly turning and pushing the people and objects with it. They "want to" continue straight with their acquired speed, but that would require them to "break through" the drum wall. This wall exerts a normal force to avoid this, and this normal force causes them to accelerate. The fact that this happens constantly and continuously around a turn gives the circular motion and makes us denote this acceleration centripetal.
A: I think you are asking about the vertical force, not the normal force which is horizontal.
If the wall is vertical then static friction is the only force which opposes gravity. The riders are pressed against the wall because of centrifugal force. Normal reaction force equals the centrifugal force. The maximum tangential force $F$ which static friction can provide increases with normal reaction $N$ : $F \le \mu N$ where $\mu$ is the coefficient of static friction. When the centrifugal force is high then static friction is large enough to equal the weight of the rider, preventing him/her from sliding downwards. 
The riders start with their feet on the floor. As the speed of the drum increases the static friction provided by the wall increases. They can climb up the wall and lie down on it. When the drum stops rotating there is no centrifugal force and no normal force. The static friction force falls to zero, and the riders slide down the wall. 
If the walls are not rough then $\mu$ is small. Then static friction is not large enough to support the weight of the riders, so they cannot climb up the wall, and slide back down if they try.
This stunt can also be performed if the walls slope outwards, at a small angle $\theta$ to the vertical, even if they are smooth. This also happens with banked roads - see How is circular motion possible on a banked road when there is no Friction? In this case there is no static friction force, only the normal force. There is a component of normal force in the vertical direction ($N\sin\theta$), which opposes gravity. Meanwhile the component of normal force in the horizontal direction ($N\cos\theta$) provides the centripetal force required to keep the riders moving round in a circle.  
