Decision trees are Machine Learning models that can be applied to Classification or Regression problems. They try to separate by doing splits, so they use if/then conditions using all the fields in your Dataset to separate the data into the classes or numeric ranges. They are a good choice as base model, because they are easily interpretable and provide not only predictions but also the associated confidence and the fields importance.
To learn about all their available configuration options using BigML's Dashboard, you can check the corresponding section of the Models documentation. Also the Models API documentation contains the information about the attributes that need to be specified to configure your source programmatically.