Dicts and other objects use hashes to store and retrieve items really quickly. The mechanics of this all happens "under the covers" - you as the programmer don't need to do anything and Python handles it all internally. The basic idea is that when you create a dictionary with {key: value}, Python needs to be able to hash whatever you used for key so it can store and look up the value quickly.

Immutable objects, or objects that can't be altered, are hashable. They have a single unique value that never changes, so python can "hash" that value and use it to look up dictionary values efficiently. Objects that fall into this category include strings, tuples, integers and so on. You may think, "But I can change a string! I just go mystr = mystr + 'foo'," but in fact what this does is create a new string instance and assigns it to mystr. It doesn't modify the existing instance. Immutable objects never change, so you can always be sure that when you generate a hash for an immutable object, looking up the object by its hash will always return the same object you started with, and not a modified version.

You can try this for yourself: hash("mystring"), hash(('foo', 'bar')), hash(1)

Mutable objects, or objects that can be modified, aren't hashable. A list can be modified in-place: mylist.append('bar') or mylist.pop(0). You can't safely hash a mutable object because you can't guarantee that the object hasn't changed since you last saw it. You'll find that list, set, and other mutable types don't have a __hash__() method. Because of this, you can't use mutable objects as dictionary keys:

>>> hash([1,2,3])
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unhashable type: 'list'

Eric Duminil's answer provides a great example of the unexpected behaviour that arises from using mutable objects as dictionary keys

Here are examples why it might not be a good idea to allow mutable types as keys. This behaviour might be useful in some cases (e.g. using the state of the object as a key rather than the object itself) but it also might lead to suprising results or bugs.

Python

It's possible to use a numeric list as a key by defining __hash__ on a subclass of list :

class MyList(list):
    def __hash__(self):
        return sum(self)

my_list = MyList([1, 2, 3])

my_dict = {my_list: 'a'}

print(my_dict.get(my_list))
# a

my_list[2] = 4  # __hash__() becomes 7
print(next(iter(my_dict)))
# [1, 2, 4]
print(my_dict.get(my_list))
# None
print(my_dict.get(MyList([1,2,3])))
# None

my_list[0] = 0  # __hash_() is 6 again, but for different elements
print(next(iter(my_dict)))
# [0, 2, 4]
print(my_dict.get(my_list))
# 'a'

Ruby

In Ruby, it's allowed to use a list as a key. A Ruby list is called an Array and a dict is a Hash, but the syntax is very similar to Python's :

my_list = [1]
my_hash = { my_list => 'a'}
puts my_hash[my_list]
#=> 'a'

But if this list is modified, the dict doesn't find the corresponding value any more, even if the key is still in the dict :

my_list << 2

puts my_list
#=> [1,2]

puts my_hash.keys.first
#=> [1,2]

puts my_hash[my_list]
#=> nil

It's possible to force the dict to calculate the key hashes again :

my_hash.rehash
puts my_hash[my_list]
#=> 'a'

A hashset calculates the hash of an object and based on that hash, stores the object in the structure for fast lookup. As a result, by contract once an object is added to the dictionary, the hash is not allowed to change. Most good hash functions will depend on the number of elements and the elements itself.

A tuple is immutable, so after construction, the values cannot change and therefore the hash cannot change either (or at least a good implementation should not let the hash change).

A list on the other hand is mutable: one can later add/remove/alter elements. As a result the hash can change violating the contract.

So all objects that cannot guarantee a hash function that remains stable after the object is added, violate the contract and thus are no good candidates. Because for a lookup, the dictionary will first calculate the hash of the key, and determine the correct bucket. If the key is meanwhile changed, this could result in false negatives: the object is in the dictionary, but it can no longer be retrieved because the hash is different so a different bucket will be searched than the one where the object was originally added to.