This is not just an Android thing, the Java SDK has the same recommendation:
Note: It is generally a good idea for comparators to also implement java.io.Serializable, as they may be used as ordering methods in serializable data structures (like TreeSet, TreeMap). In order for the data structure to serialize successfully, the comparator (if provided) must implement Serializable.
So the idea is that because a TreeMap is serializable, and the TreeMap can contain a Comparator, it would be good if the Comparator is also serializable. The same applies for all elements in the collection.
You can safely ignore this unless you use serialization in that way.