Both play a part in image sharpness.

The focus point is what tells the camera where you want the focus to be. This is where your image will be it's sharpest.

The DOF will determine the range (min and max distance from the camera) in which things will be close enough to in focus to be considered acceptably sharp. The more shallow the depth of field, the smaller the range (distance from the camera also impacts this).

For example, portraits are typically taken with a shallow DOF (large aperture) so only the subject is in focus and background gets a nice blurry effect (bokeh).

On the flipside, landscapes will typically be taken with a deep DOF (small aperture) so that objects in the foreground and background are all in focus.

You can try this yourself. (The faster the lens i.e. the lower the f stop number, the better).

• Pick a scene with object at varying distances. A picket fence viewed from and angle for instance. Stand close to the fence, say 1 metre, and point the camera at 45 degree angle at the fence.
• Set your camera to use all its AF points.
• Set your camera to its lowest f stop, I will assume it is f3.5 (if you have a faster lens then go lower).
• Press your shutter half way to focus and notice how many AF points light up (in focus).
• Repeat but choose a higher f stop each time. You will notice that more of the fence will show up as in focus.

You can try the same experiment with changing the distance between the camera and the subject as well to see the impact.

Of course, you can also do the same experiment and actually take pictures instead, but in that case, choose the same focus point all the time so you will see the difference in how much is in focus as you change the f stop.