How is a single element of the training set called?
The term you are looking for is "Example".
Source: Martin Zinkevich, Research Scientist at Google (http://martin.zinkevich.org/rules_of_ml/rules_of_ml.pdf)

Instance: The thing about which you want to make a prediction. For example, the instance might be a web page that you want to classify as either "about cats" or "not about cats".

Label: An answer for a prediction task ­­ either the answer produced by a machine learning system, or the right answer supplied in training data. For example, the label for a web page might be "about cats".

Feature: A property of an instance used in a prediction task. For example, a web page might have a feature "contains the word 'cat'".

Example: An instance (with its features) and a label.