Light rays can change direction when they encounter small particles, a phenomenon called scattering.
If you smash a clear ice cube, the pile of small pieces appears brighter and whiter than the whole cube. This is because the shards scatter light more extensively than one whole cube. This kind of scattering also happens in clouds.
Clouds are made of small water drops and small ice crystals that scatter light from the sun in all directions. These individual drops and crystals are clear. It is the multitude of drops and crystals that make a cloud look white during the day because the small particles scatter the sun’s light in all directions.
The brightness of the cloud is a function of how much of the sun’s energy is leaving the part of the cloud you are viewing. If you are looking at a thin cloud, then there are few water particles to scatter the light, so the cloud will not look bright white.
The sides of a cloud often look bright white because lots of light is scattered out the sides. If the cloud is very deep, then only a small amount of light escapes out the bottom of the cloud, and so cloud bottoms often appear grayish.
If one cloud contains very large drops and another contains very small drops, the cloud containing the small particles will appear brighter. Again, much like the case of the smashed ice cube — small particles scatter the sun’s light in all directions more efficiently than do large particles.