Not everyone does, but those who do, do so because of a phenomenon called binocular rivalry.
If you look through a sight with the left eye, what you see is not identical with what you see with the right, and the two images compete, rather than blending, as they normally do when you look at something with both eyes.
For example, if the left eye is shown only vertical lines and the right eye only horizontal lines, you might think you would see a screen pattern, but in fact you would see patches of vertical lines intermingled with patches of horizontal lines.
Some people can mentally suppress the competing image, but some find it uncomfortable, so they close one eye.
In aiming, most people tend to use the dominant eye, which generally but not always has better vision.
If the eyes differ in focal length, some may use one eye for long distances and the other for short distances.