This phenomenon has to do with the actual structure of our eyes.

There are two types of cells in our eye that let us see. They are called rods and cones and they are located in the retina at the back of the eye. The cones are highly sensitive to color and detail but do not function well in dim light. The rods are extremely sensitive to light but can't pick up very much detail. The rods generally outnumber the cones 10 to 1, except in a small region in the very center of the eye called the fovea, which contains an enormous number of cones. This is why when we read, we usually focus on just a very small area of the page.

Try to read a book by looking at an entire page at once, it's impossible! Unfortunately, the fovea contains almost no rods. So when you look directly at your stars at night, the cones in the fovea can't pick up any light. You have to look slightly to the side so that your eye's rods can see them.

Great question! You might notice the same effect looking at real stars outside too. Some faint starts are visible out of the side of your vision, but not if you look directly at them.

Our eyes have two main types of light sensors (also called photoreceptors). They are called rods and cones. Cones sense color and are located in the center of the retina (the back part of the eye onto which light is focused). Rods only sense light intensity, but are much more numerous and sensitive. They are located around the edges of the retina. Therefore, our vision is actually much more sensitive around the edges than in the center (but we do like seeing in color).

Rod sensitivity is also why we can continue to see in a dimly lit room, but cannot distinguish colors.

Read more about it here.