In the context of machine learning, a metric is any number that we care about. An objective is a specific type of metric that a machine learning system attempts to optimize.
Technical Metrics
​Accuracy is the most common (and easy to understand) metric but tracking only accuracy will paint an incomplete picture of how your model is performing. There are several other well-established metrics that provide deeper insight into model performance.
Metrics are often specific to the type of machine learning problem or model. Important and widely adopted metrics include: Accuracy, Loss, Confusion Matrix, AUC (Area Under ROC curve), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and R Square.
Correlating to Business Metrics
Machine learning metrics are often directly correlated to business metric. One example would be assigning a dollar value to false positives in a classification model. Here's a great example of how AirBnB measures the performance of their fraud prediction algorithm in dollars.