Product metrics are indicators that show how users interact with a product. They are derived from measurements and often have a numeric component of time, ratio, rate, etc. For example, your activation rate measures how well your efforts are increasing the number of new active users. Feature usage helps you track how a customer uses a given feature, which can provide insight into what part of your product provides the most value or is a critical action in the customer journey. And tracking whether users are repeatedly coming back to your product helps you understand whether your business is growing sustainably.
Product metrics give you information on how to improve your product. Tracking product metrics as part of a controlled experiment before and after you make changes tells you whether or not those changes worked. This process of measuring, experimenting, and assessing is how you progressively iterate your product.