Unlike many forms of Product, objects and businesses, we have the ability to understand every single thing a user does when using a software product.
Using Analytic software, we can observe user behaviours and interactions, helping to identify trends and that help tell the user story and further inform and enlighten the Product development process.
The data points and metrics that emerge are quantifiable, and can help prove if design and product changes are having a positive or negative effect.
However, whilst the raw data is helpful, it doesn't necessarily explain why a user does something and won't predict if a user will do something. It can only record when they have done something - and just because they have done something, that might not have been caused by a change - correlation between metrics doesn't mean that one action caused another.
The biggest part of using analytics is to keep track of business goals, conversions or sales for example, and it will help greatly with tweaking and improving things - but remember, it is not the foundation of creating a great product and user experience, just part of it.