Try to think the rope made up of small solid balls connected with springs. When you make the bump as shown in your picture the springs are expanded. Now you let go of it. The rising ball applies force upward to the ball on its right. The already expanded springs soon tend to decompress again. In doing so the the falling ball applies a downward force to ball at left. This is how the bump shape moves in the forward direction. The balls at the right keep providing upward force for the forth coming right balls.
When the wave reaches the end which is clamped the right most ball has to remain fixed. All the energy reaches the spring connected with the right most ball. The second last ball will remain high until half of the bump doesn't disappear. Now if there were no clamp the rest half bum had to fall usually. But now it will fall usually + the last spring will decompress very hard and will shake the half bump in downward direction. This will make a reflected bump in the downward direction.
You can similarly conceive the interference of waves on a rope with this model.