I don't really understand the purpose of Static fields

Adding on to what Steven said, I think that a static method is a great way to accomplish something that needs to be done in multiple locations like Math.Sqrt. We shouldn't have to create an instance of the Math class each time we want to use the logic to get the square root of a number, but we also don't want to have to write that same logic all over our application. Instead we use a static method that performs the calculation, but doesn't require a new object to do so.

Not requiring an instance is a huge bonus for helper methods, but that's kinda of a side effect. The main goal is to have attributes/properties and methods that belong to a class rather than the instance. As to why this could be useful, just think of any scenario you might want information/control over the class or all instantiated objects of that class.

For example, counting or keeping tracking of every object created, say for memory management, so you could have a pool of reusable objects instead of destroying and creating new ones every time. Or for the complete opposite, you want to make sure there's only ever one instance of that class at a single time, and an easy way to make that possible is to make the constructor private, and encapsulate the type creation into a Factory Method (which is static) and makes sure that a new instance is only ever created once. That's actually a very common design pattern called singleton;