Basically, when you serialize arrays or objects you simply turn it to a valid string format so that you can easily store them outside of the php script.
Note for object you should use magic __sleep and __wakeup methods. __sleep is called by serialize(). A sleep method will return an array of the values from the object that you want to persist.
__wakeup is called by unserialize(). A wakeup method should take the unserialized values and initialize them in them in the object.
For passing data between php and js you would use json_encode to turn php array to valid json format. Or other way round - use JSON.parese() to convert a output data (string) into valid json object. You would want to do that to make use of local storage. (offline data access)