Persistent java object means, the state of the object can be stored to the persistent storage (eg. hard drive) for later use. State of java object means at particular instance what information its members are consisting. For object persistence to be possible, the class must implement the Serializable interface. This interface does not have any method to be implemented that is why called marker interface.
how does it relates to transient variables?
Sometimes you may want some of your members not required to be saved as part of object state. You make those member variables transient so that while serialzation takes place, all the members get serialized except transient variables. Static members are not part of object, they are for class, so no serialization for them also.