Random forests provide an improvement over bagging by doing a small tweak that utilizes de-correlated trees. In bagging, we build a number of decision trees on bootstrapped samples from training data, but the one big drawback with the bagging technique is that it selects all the variables. By doing so, in each decision tree, the order of candidate/variable chosen to split remains more or less the same for all the individual trees, which look correlated with each other. Variance reduction on correlated individual entities does not work effectively while aggregating them.
In random forest, during bootstrapping (repeated sampling with replacement), samples were drawn from training data; not just simply the second and third observations randomly selected, similar to bagging, but it also selects the few predictors/columns out of all predictors (m predictors out of total p predictors).
The thumb rule for variable selection of m variables out of total variables p is m = sqrt...