Here, a chemical is added that causes tiny suspended particles to clump together. Usually, these flocs settle out just like large size sediments. But if they escape, filters down the line catch them. Chlorine is a chemical that kills microorganisms. In drinking water, the contaminations are low enough that often you can't even taste it.
Water is pumped through large tanks filled with fine sand, called rapid sand filters.
As the water flows through the spaces between the sand grains suspended particles and dead microbes get trapped. Sometimes, crushed anthracite coal is used in addition to sand. Because the coal grains carry a charge on their surface, they act like tiny magnets attracting other charged contaminants. Aeration is exactly what it sounds like, the addition to air in water. When sprayed through large fountain like devices, water not only gains a great deal of oxygen, but any volatile compounds that may have been in the water escape into the atmosphere.