Clear beer is often a goal for many homebrewers, the standard being set by the commercial brewers. With modern brewing techniques and common industrial practice we have come to expect our beer to be crystal clear. When homebrewing, clear beer is not common. In reality, most homebrews are cloudy.
The two main culprits of cloudy beer are yeast and proteins.
As the yeast near the end of their job (i.e. when fermentation is ending due to lack of sugars) the single cells of yeast will clump together in groups of thousands and settle out. This is known as flocculation. Different yeasts flocculate differently. Some yeasts settle out nicely and others do not. One strategy to get more yeast to settle out is to cool the beer (such as lagering) before bottling or kegging.
The other culprit of cloudy beer are proteins along with polyphenols and lipids (fats). While proteins are not necessarily small molecules, they are small enough to remain in suspension.
Beer can be clairified using Irish moss, a fining agent. Fining agents all work by making the smaller molecules aggregate into larger particles so they settle out of solution. This can be mathematically described by Stokes Law:
Where v is the rate of sedimentation, r1 is the density of the particle and r2 is the density of the wort, r is the radius of the particle, g is 9.8 m/sec2 (a.k.a. acceleration due to gravity), and h is the viscosity of the medium. In other words, as the density and size of the particle increases it will settle out faster. In addition, a thinner wort will allow settling to occur faster.
Irish moss is Atlantic red seaweed that contains k-carrageenan:
The k-carrageenan is a polymer of β-D-galactose-4-sulphate-3,6-anhydro-a-D-galactose. It is similar to starch or cellulose (i.e. comprised of thousands of carbohydrates). The negatively charged sulfate groups are thought to interact with the proteins in suspension. As the wort cools, more and more proteins interact with the k-carrageenan and the k-carrageenan adopts a more compact structure. The result is the molecular equivalent of marbles in syrup. After the churning of an active fermentation ends (4-5 days) the carrageenan-protein chunks settle out with the yeast.
Homebrewed beer is still often cloudy, but Irish moss does make a noticable difference.
 He he he he, I said flocculation.
 Yes, seaweed.