What you looking at is a small segment of the string which you will show will undergo oscillatory motion at right angles to the string in its position of rest.
So in the end you are looking at a transverse wave.
The curvature of the segment changes along its length and so there is a net force downwards acting on the segment trying to restore it to its equilibrium position.
As there is a net force downwards the segment accelerates downwards.
The segment that you are looking at is linked to adjacent segments of the string.
If the wave was travelling to the right then the motion of the segment to the left of the one you are considering would be advanced in phase and the the segment to the right would be retarded in phase relative to the segment under consideration.
So the diagram is indeed a wave profile, a snapshot of the string at an instant of time.
If you took the photograph a little later in time for a right travelling wave you would find the the segment to the right of the segment under consideration would look like the segment under consideration.
So as time goes on the string changes shape with each segment of the string undergoing oscillatory motion but with a progressive phase difference for adjacent segments along the string.
Some of your segments are highlighted in red and you will note that although you get the impression of a wave travelling to the right each of the rod dots is actually oscillating up and down.
Also note that phase difference for dots either side of the red dots.
The diagram also shows you how a wavelength is defined.