Definitions

Some fairly basic definitions:

Observation: the process of recording the weather, the temperature, dew point, clouds (heights/amounts/types), presures (sea level and tendancy), wind (mean and gust speeds and direction), visibility and weather (current and recent). Much of this can be automatically recorded but visibility, clouds and weather the human observer is still by far superior.
SYNOP: The code used for met observations.
METAR: The code used for aviation observations. The METAR uses less information and groups than the SYNOP but includes all the relevant information for aviation. There are slightly different rules for the civil and military aviation, always based on flight safety, so if you see two reports from adjacent airfields, one civilian and one military, and they seem different, it's usually just the different ideas of what is safe. Suprisingly the military one is the more conservative.
Forecast: what we think will happen. Two things, we DON'T order or control the weather, and we DON'T get it right all the time. No one does. There are two main types of forecast, deterministic and probabalistic.
Deterministic: The forecaster gives one option, "this is what will happen." For example, "the temperature will be below -4 tonight" or "the wind will be south-westerly." This style is easier for the average customer to understand but if it is slightly wrong it is completely wrong. The forecaster needs to make an absolute decision about what they are putting into their forecast.
Probabalistic: The forecast includes a range of options with a quantitive value of the probability of each outcome. For example, "a 30% chance of showers during the forecast period," or "a 90% risk of funnel clouds." This last is not a likely forecast, if we could give this accuracy, alot of people would be happier. While this type of forecast can seem like the forecaster is hedging their bets but in fact it gives them an option to express what is possible. If the customer knows what they are looking at this form gives them more information but is harder to fully understand and communicate.
Model: Bloody clever people, starting with Lewis Fry Richardson in 1914, have found that the atmosphere can be approximated by using equations. Lots of equations. With things like partial differentiation and so many constants that they almost run out of letters using the Roman and Greek alphabets, upper and lower cases. Oddly enough, to get the accuracy and frequency needed, the modern models use some of the world's most powerful computers to produce the numeric weather products (N.W.P.) that is so useful. Basically, after 36 hours our principle tool is N.W.P. But there are areas and conditions under which the model doesn't perform as well, in these areas forecasters are essential. The Met Office has a global model, called "The Global Model" and a smaller scale model with a much higher reolution called "The Mesoscale Model." The guys spend ages over the names.
Ensemble Model: Take a set of conditions that are the current conditions and run the model. This is your reference. Now change the conditions slightly to give different starting conditions and run the model again. Repeat with different conditions, bound by what is possible within the climatic limits, about 50 times. If most of the results give the same solution then you can be fairly certain that this will happen, even if the starting weather is slightly off. If, however, the solutions are very different then the initial conditions will have much more impact on the outcome and your confidence in the initial run will be lower. ECMWF produces a great emsemble product.

Definitions : I'll add more as and when I feel like it.