This question is answered many times in SO, but still I will attempt to answer this .
In order to understand this concept completely, we need to understand the purpose of hashcode and equals, how they are implemented, and what exactly is this contract(that hashcode also should be overridden when equals is overridden)
equals method is used to determine the equality of the object. For primitive types, its very easy to determine the equality. We can very easily say that int 1 is always equal to 1. But this equal method talks about the equality of objects. The object equality depends on the instance variables or any other parameter (depend purely on the implementation - how you want to compare).
This equal method needs to be overridden if we want some customized comparison, lets say we want to say that two books are same if they have same title and same author, or I can say two books are equal if they have same ISBN.
hashcode method returns a hash code value of an object. The default implementation of the Object hashcode returns a distinct integers for distinct objects. This integer is calculated based on the memory address of the object.
So we can say that the default implementation of the equals method just comapres the hashcodes to check the equality of the object. But for the book example - we need it differently.
Also Equal objects must produce the same hash code as long as they are equal, however unequal objects need not produce distinct hash codes.
In case of not using a hash based collection, you can break the contract and need not to override the hashcode method - because you ll not be using the default implementations anywhere but still I would not suggest that and would say to have it as you may need it in future when you put those things in collection