Bagging (or Bootsrap Aggregating), the second prediction technique brought to the BigML Dashboard and API, uses a collection of trees (rather than a single one), each tree built with a different random subset of the original dataset for each model in the ensemble. Specifically, BigML defaults to a sampling rate of 100% (with replacement) for each model. This means some of the original instances will be repeated and others will be left out. Bagging performs well when a dataset has many noisy features and only one or two are relevant. In those cases, Bagging will be the best option.
Random Decision Forests extend the Bagging technique by only considering a random subset of the input fields at each split of the tree. By adding randomness in this process, Random Decision Forests help avoid overfitting. When there are many useful fields in your dataset, Random Decision Forests are a strong choice.
Click through for how boosted trees change this model a bit.