The advantage of the Observer pattern is that it solves specific problems related to one-to-many relationships between objects. So, if you have a core component that often changes states and has many dependencies that need to react to those changes, then the Observer pattern permits you to define a relationship between those entities and a mechanism that enables them to be notified.
Therefore, if you are unsure when to use the Observer pattern, you should analyze the relationship between your objects to determine if this pattern is well-suited for the problem you are trying to solve.