Prior to the advent of sterile filtration it was very common to have bottle sediment in wine. Decanting the wine with a candle behind the neck was the romantic way of eliminating it, with the sediment and a couple of ounces of wine left in the bottle.
A wine, even a white, can look perfectly clear and still have solids in it. The human eye can only detect particles down to a certain level. I think it is around 30 microns for someone with excellent vision. Ultrafine solids can take as much as 50 years to settle. There is a complex equation that governs settling rate, involving densities, temperature, and particle size.
When a bottle of wine sits in an environment where the temperature varies, even only by a degree or two, the wine develops convection currents. This causes the particles to gently "bump into" each other and stick together. The equation I mentioned above tells us that larger particles settle faster than smaller particles. (Think pebble vs. fine clay dust.) That's how they build up and settle out in the bottle. They were always there, they were just too fine to see.
Similarly, when you add a clarifying agent you chemically bond the particles together around the clarifier molecule, making them bigger and hastening the settling. By including clarifiers in the kits, manufacturers are helping us minimize any fine particles left in "clear" wine.
