Cumulous clouds form when the atmosphere gets unstable. For incompressible liquids, "unstable" means a high density liquid "water" is balancing precariously on a low density liquid "oil" (ignore surface tension). If a little bit of the lower density liquid rises, it will act like a "bubble", and will be pushed upward. The updraft will cause a positive feedback that pulls up more "oil". Eventually, large plumes of "oil" are rising as the "water" falls to take it's place. If you colored the "oil" white, you would see a cumulous cloud shape.
For air, the definition of "instability" is more complicated because air is compressible. "unstable" means that if you take a "parcel" of air and lift it up a little bit (Nature does this so quickly that little heat transfer happens), it will be less dense than the surrounding air. Thus it acts like the liquid case. Most instability is caused by solar radiation heating the ground and reducing the density of the low-level air.
As it rises, the cooling from the decompression (altitude) causes water to condense. The "background" air that the rising air is moving into is mainly displaced to the side and downward (to replace the air near ground level), so it remains clear. Thus, the billiowing cloud surface is the interface between the rising plume and the "background" air. The clear air in the space between clouds is in fact descending to replace the low-level air.
There is another reinforcing effect: As water condenses, it releases heat which slows down the cooling effect of decompression. This effect is stronger than the reduction of water volume as it changes from a gas to a liquid.
What about uniform mists? In this case, air rises and condenses uniformly. Something has to replace the air as it rises, and that something is a "front", a layer of air that is moving in horizontally to displace the air upward like a wedge.