Final answer:
The machine learning method being used is supervised learning, which trains an artificial neural network with labeled images to identify plant species.
Step-by-step explanation:
The machine learning technique used for training an artificial neural network with a labeled dataset is called supervised learning. In supervised learning, the algorithm is provided with input-output pairs, where the expected output (the label) for each input is known. This method allows the model to learn the mapping from the input to the output. In the context of a smartphone application that identifies plants, the neural network is trained with images of plants (the input) that are already labeled with their species names (the output). After sufficient training, the model should ideally be able to predict the species of a new, unseen plant image by generalizing from the labeled examples it was trained on.