Random Forests are a type of ensemble method for predictive modelling and inference. Ensemble methods take a different approach to classical statistical methods by building an ensemble of related (but different) models. The hope, and in many cases the reality, is that incorporating information from many `weak' models provides better results than producing a single `strong' model, which uses all of the information in the data simultaneously. Essentially, ensemble methods perform thousands of experiments on the data by seeing what happens when aspects of the data are perturbed (e.g. removed from the analysis). The results of these experiments are then collated, and we hope to learn something by altering the data many times over and gathering the results together.
The `weak' models in Random Forests are very simple models called decision trees (many trees make a forest)Decision trees work by attempting to find the best place to `split' a variable (or a few variables) so that the resulting rule produces a prediction most in accordance with the data. For example, a very simple decision tree would look to find the age which best separates retired from working people given data on retirement ages, or the expression level of some gene best separating dividing from resting cells. Usually, decision trees are built by taking into account a number of variables and combining these simple decision rules to obtain a better prediction. Random Forests build many such trees, each time using only a subset of the available predictors and a subset of the available data. Each of these trees has a say in the final prediction, meaning that quite complex patterns and interactions can become apparent, which are not available (at least automatically) in classical statistical methods like linear regression or Cox Proportional hazards.