From The weather Vane Wiki
Anomaly - noun -variation, deviation from the norm, an occurence outside the standard or expected condition or measurement.
In weather and meteorology the term "anomaly" may have different applications.
An example of one common application is the use of the word to describe a deviation from an average course of observed measurements taken over a period of time to establish a "standard" or "norm". Thus the difference between the currently observed Sea Surface Temperatures (SSTs) and an standard value obtained by averaging measurments over a period of prior years may be called the "anomaly".
For example, if the historical average or standard SST for a reagion on a given day in the month of July was given as 29 degrees C. (Celsius) and the current temperatures on the same date were measured as 32 degrees C. the "Anomaly" measurement would be calculated as: 32 C. - 29 C. = +3 C. and indicate that current temperatures for that region deviated from the "norm" or standard by being 3 degrees warmer.
Likewise, if current temperature was 27 C., the calculation would produce a negative number....27 C. - 29 C. = -2 C. indicating the anomaly is that the current temperature is 2 degrees C. cooler than the average used as the standard. An Anomaly measurement of "0" means that there is no significant deviation from the average or standard used.
Putting a quantitative analysis on an anomaly makes it easy to plot on graphs and maps to show where anomalies are occuring. Here is an example of SST anomalies plotted on a map. 
Such anomaly analysis of average measurements can be used to give information about various weather factors measured over a period of time, such as storm frequency, storm magnitude, windspeed and /or direction, precipitation, snowfall, air or earth temperatures, barometric pressure readings and many more.
If an anomaly repeats over time, it may signal the beginning of a trend toward the anomaly, ie, toward warmer or cooler SST's in a given region. In such case, eventually the anomaly would become part of the "norm" or average calculations and the "norm" may be adjusted to reflect the trend. The anomaly might then cease to be an "anamoly" per se.
Another way that the term "anomaly" may be used in weather and meteorology in a more general way to describe a single major deviation or "freak" event that cannot be readily explained. Such an event might be the convergence of factors to produce a storm that caused a three foot snowfall within 48 hours in coastal Georgia in July...surely that would be an "anomaly" in this day and age...but 2000 years from now, who knows?? That might be "average" weather behavior for that area by that time.
Such single "freak" events would be considered an "anamoly" because historically, they are unheard of and range far outside what might be expected in the area or because the probability of all the factors necessary to producing such a storm coming together at the same time is so low as to be very unlikely. But if such "unheard of" events increase in regularity or are repeated in the future, they may fit into theories of a trend or cycle or other explanation and will no longer be an "anomaly".
As another example of general use of the term, the entire 2005 hurricane season might be described as an "anomaly" due to the high number and magnitude of the tropical storms and hurricanes that developed which is far above averages for the season. The question many meteoroligists are considering in 2006 is whether the high activity in the 2005 hurricane season will turn out to be an "anomaly" or whether it signals the beginning of a trend of more active seasons, or fit into a "cycle". An event that is truely an "anamoly" will not readily fit into trend or cycle analysis over time or be readily explained by other weather factors that are in an established trend or cycle. Likewise, a season in which no tropical depressions, tropical storms or hurricanes developed at all, anywhere, might be called an "anomaly" because it is expected from past observations that at least some will occur in each hurricane season.
It is important when evaluating the significance of any anomaly to understand what is being used as the "standard" or "norm" and how it was derived. Usually, the significance of a anamoly in any given measurement will be greater if the standard has been derived by averaging in a number of observations over a long period of time, and also if there has already been a "standard deviation" calculation applied. A "standard deviation" is a statistical calculation taking into account that in some areas of measurement, it is "normal" for certain deviations to occur and the standard deviation shows what deviations might be in the "normal" range as occasional events.