When looking at the stars why can I see the fainter stars better out of the corner of my eye?

Because the eye has two kinds of receptors, cones for fine resolution and color and rods for dim light, and the rods tend to be located around the periphery, for viewing the edges of the field of vision.

Cones are extremely good at high definition and for precise positioning of pinpoints of light. Rods don’t give nearly as fine resolution and don’t distinguish colors, but are much more sensitive. In effect, rods serve as night-vision sensors.

The result is that when you go out at night, you can clearly see the bright stars and planets at the center of your eye, but you can see the fainter ones out of the corner of your eye. Astronomers call this averted vision.

For example, if they look with the unaided eye straight at a galaxy they know is there, they may not see it, but if they look off to one side, they can easily see the fuzzy gray patch that is the galaxy.

Cameras, too, tend to give up resolution and sensitivity to color when they achieve better sensitivity to low light levels.