Why is the sky sometimes gray?

The sky turns gray when clouds spread between us and the sun. Their water droplets and ice bits scatter all colors of sunlight together, instead of mostly scattering blue. In thick clouds, much less light reaches the underside, so the cloud ceiling looks dim and gray from below.

That flat gray light is why cloudy days have softer shadows. A cloud layer acts like a huge shade, spreading daylight around the whole sky. When the droplets are close to the ground, your family is seeing fog: a cloud low enough to walk through.