Definition of "Effective population size"
Short answer: The effective population size of a population is the corresponding population size of a idealized (fisherian) population that would function in the same way with respect to genetic drift and inbreeding as the focal population under interest.



Long answer, below.

Definitions:

Heterogenity: the probability that two randomly sampled alleles in the population are identical (identical by descent).

Census Population Size: The census population size ($N$) is the number of individuals in the population.

Fisherian population

A fisherian population is an idealized population of size $N$, where all individuals mate at random, there is no selection, there is no population structure, there is no mutation and generations are non-overlapping. There probably are no perfectly fisherian populations in nature!

Genetic drift causes a decrease in heterogeneity. As the genetic drift is a function of the population size (see this post) this decrease of heterogeneity is a function of the population size. The heterogeneity at time $t$ is:

$$ H_t = H_{0}\left( 1-\frac{1}{2N} \right)^t$$ 

, where $H_0$ is the heterogeneity at $t=0$. You can verify by yourself that as $t$ increase , $H_t$ decreases. Also, as $N$ decreases, $H_t$ decreases. In other words, the longer you observe, the more heterogeneity gets lost and the smaller is the population, the higher is the loss of heterogeneity.

Effective Population Size

Let Pop_A be a real population. The effective population size ($Ne$) of Pop_A is the size of an idealized fisherian population that would have the same loss of heterogeneity than Pop_A.

You can read the above sentence twice to make sure you understand it. It basically is the definition of the concept of effective population size.

In other words: Let $N$ be the population size of Pop_A. If Pop_A is a perfect fisherian population, then its loss of heterozygosity through time is given by:

$$ H_t = H_{0}\left( 1-\frac{1}{2N} \right)^t$$ 

If Pop_A is not a perfect fisherian population, then it's decrease in heterozygosity is greater than the one given by the above formula. The decrease in heterozygosity of Pop_A corresponds to the decrease of heterozygosity of an idealize fisherian population of a different size. This size is called the effective population size $Ne$. So, we can rewrite the loss of heterogosity through time of Pop_A as:

$$ H_t = H_{0}\left( 1-\frac{1}{2Ne} \right)^t$$ 

(Note $N$ has been replaced by $Ne$)

, where $Ne$ is the effective population size of Pop_A.

Usually $Ne &lt; N$, meaning that a real population undergoes more genetic drift than does a fisherian population of the same census size. There are many reasons that may yield a real population to have a higher drift than it would be expected with the same census size but respecting the assumptions of the fisherian population. Below I discuss three reasons:

Examples

Unequal sex-ratio

Think as a first example of a population where the sex-ratio is extremely biased to the point of having one male for 99 females. In such population, half of the alleles of a given locus at the next generation will come directly from the father. In such situations, the genetic drift is much higher than what would be expected from a fisherian population of size 100. Therefore $Ne&lt;N=100$. To calculate $Ne$ when the sex-ratio in unequal you can use this formula:

$$Ne=\frac{4N_mN_f}{N_m+N_f}$$

, where $N_m$ and $N_f$ are the census populatino size of males and females respectively. You can verify that when $N_f = N_m$, then $N_f + N_m = N = Ne$.

Variation in population size through time

If your population size varies throughout a given time (a year for example) and that at time $t=3$ (a given period of the year) the census population size is given by $N_i$, then the effective population size is:

$$Ne = \frac{1}{\frac{1}{t}\sum_{i=1}^t\frac{1}{N_i}}$$

This is particularly relevant for insects for example which population size varies a lot between seasons.

Selection

Think now of a population where there is a great variance in fitness (there is selection). In such population, maybe all offspring will be produced by only a tenth of the current population. As a result the effective population is ten times smaller than the census population size.



You can probably find all these informations from wikipedia: http://en.wikipedia.org/wiki/Effective_population_size

Let me know if the concept of the effective population makes more sense to you now.