Variation:  If all members of a species were identical there could be no evolution; which organisms survive and reproduce would be determined solely by chance and would not result in any changes over time.    

But large amounts of empirical data indicate that organisms of the same species are not genetically identical.  For example, an analysis of human DNA reveals that when we compare two unrelated individuals, we can expect one sequence difference for every 1200 base pairs we examine.   Since each human cell has approximately 6,000,000,000 base pairs of DNA, that is a lot of differences (more here).
 

Although some traits are difficult to measure, others are simple to quantify.  How smart, or good, or funny, or sensitive a person is depends upon how you define "smart" or "good" or "funny" or "sensitive" - and probably exactly when, where, and how you make your measurements. 

These traits, although real, are difficult to quantify; it may be difficult or impossible to study them scientifically. 

On the other hand, there are traits that are easier to measure.  Height, body or brain weight, reaction times, tooth size, resistance to specific pathogens, or hair color– these are traits that can be measured in a quantitative manner.

If we were to measure a large enough population of organisms with respect to one of these "quantifiable" traits, we would determine the frequency distribution for the trait. 

For many traits, this distribution is a normal distribution.  You can identify a normal distribution because it is symmetrical around a peak; the peak value is generally the mean of the distribution. 

Generally traits that fall into a normal distribution are determined by the action of multiple genes.  

On the other hand some traits, such as blood type (that is, whether you have O, A, B or AB blood type), are discontinuous.  Such traits are generally controlled by variations in one gene. 

Not all traits effect the ability of an organism to survive or reproduce successfully.  Natural selection acts directly on traits that alter reproductive success.   

At the same time, it is possible for two traits to be linked so that selection of one leads to selection of the other.   The genes involved can be located near one another on a particular chromosome or it may be that the process of producing the selected trait also produces the other "non-selected" trait. 

If this is the case, then the non-selected trait will be found in the population not because it is in and of itself advantageous, but because it necessarily accompanies the selected trait. 

This is worth keeping in mind whenever someone tries to explain the presence of a particular trait based on its presumed benefits.

• Why is it that the more genes that determine a trait, the more continuous is the distribution of that trait in a population?

In the case above , with each generation, individuals that carry deleterious forms of the trait are likely to produce fewer off-spring than those that do not.  Over a number of generations, the frequency of organisms with the disadvantageous trait will decrease.  This process is known as directed selection.

• Does directed selection ever stop?  That is, does the mean ever stop changing? 

Conservative selection:  Another possibility is that individuals with traits at either end of the population distribution are at a reproductive disadvantage compared with organisms that are closer to the mean. With each generation, the contribution of these "outliers" to the next generation will be reduced.   The distribution mean will remain constant, but the standard deviation will decrease.

The stronger the disadvantage the outliers face, the narrower the distribution will become.  In the end, the size of the standard deviation will reflect the rate at which new variation enters the population.

• Why does variation not completely disappear in the face of conservative selection?

Disruptive selection:  A third possibility is that the organisms with traits at the extremes of the population distribution actually have a reproductive advantage over those nearer the mean. 

This type of behavior would tend to expand the population distribution, while mating between organisms at the extremes would tend to bring the population distribution back to the original state. 

If organisms at the extremes preferred to mate with organisms with the same form of the trait, the population would split into two. 

• Can you develop a scenario that would lead to disruptive selection?