From Unofficial BOINC Wiki
In physics, a statistical ensemble is a large set of (mental) copies of a system, considered all at once; each copy of the system representing a different possible detailed realisation of the system, consistent with the system's observed macroscopic properties.
A climate ensemble involves slightly different models of the climate system. There are at least 4 different types, to be described below.
The aim of running an Ensemble is usually in order to be able to deal with uncertainties in the system. An ultimate aim may be to produce policy relevant information such as a Probability Distribution Function (pdf) of different outcomes. The Climateprediction.net (CPDN) home page says "climateprediction.net should, for the first time, tell us what is most likely to happen". This means they are hoping to be able to produce a pdf.
This is proving to be very difficult in general for climate researchers due to a number of problems. These include:
1. The ensemble has to be wide ranging to ensure it covers the whole range where the climate models may be good.
2. Measuring what is a good model is difficult. This may need to consider not only errors in the observation but also in the model.
3. Any prior assumptions about distribution can influence the pdf produced.
 Perturbed Physics Ensemble
Perturbed physics ensembles form the main scientific focus of the Climateprediction.net (CPDN) project. Modern climate models do a good job of simulating many large-scale features of present-day climate. However, these models contain large numbers of adjustable Parameters which are known, individually, to have a significant impact on simulated climate. While many of these are well constrained by observations, there are many which are subject to considerable uncertainty. We do not know the extent to which different choices of parameter-settings or schemes may provide equally realistic simulations of 20th century climate but different forecast for the 21st century. The most thorough way to investigate this uncertainty is to run a massive ensemble experiment in which each relevant parameter combination is investigated.
 Initial Condition Ensemble
Initial condition ensembles involve the same model in terms of the same atmospheric physics parameters and forcings, but run from variety of different start dates. Because the climate system is chaotic, tiny changes in things such as temperatures, winds, and humidity in one place can lead to very different paths for the system as a whole. We can work around this by setting off several runs started with slightly different starting conditions, and then look at the evolution of the group as a whole. This is similar to what they do in weather forecasting.
Having an initial condition ensemble can help to identify natural variability in the system and deal with it.
 Forcing Ensemble
A model can be subjected to different forcings. These may correspond with different scenarios such as the SRES scenarios.
 Grand Ensemble
A grand ensemble is an ensemble of ensembles. There has to be at least two nested ensembles. This is best illustrated in the following diagram.
Weather forecasting uses initial condition ensembles.