When would a frozenset be useful?

frozenset() objects can be used as dictionary keys and as values inside of set() and frozenset() objects, where set objects cannot. set() values are mutable and not hashable, frozenset() values are immutable and are hashable.

They are to set objects what tuple objects are to list objects.

Demo:

>>> s = set([1, 2])
>>> fs = frozenset(s)
>>> adict = {}
>>> adict[s] = 42   # a set as key does not work
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unhashable type: 'set'
>>> adict[fs] = 42  # a frozenset as key works
>>> s.add(s)        # a set as value in a set does not work
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unhashable type: 'set'
>>> s.add(fs)       # a frozenset as value in a set works

Recent Python versions will optimize the use of a set literal:

if somevar in {'foo', 'bar', 'baz'}:

by storing a frozenset() constant with the bytecode:

>>> import dis
>>> dis.dis(compile("if somevar in {'foo', 'bar', 'baz'}: pass", '<stdin>', 'exec'))
  1           0 LOAD_NAME                0 (somevar) 
              3 LOAD_CONST               4 (frozenset({'foo', 'baz', 'bar'})) 
              6 COMPARE_OP               6 (in) 
              9 POP_JUMP_IF_FALSE       15 
             12 JUMP_FORWARD             0 (to 15) 
        >>   15 LOAD_CONST               3 (None) 
             18 RETURN_VALUE         

because the set literal cannot be mutated anyway; this makes using sets to test against very efficient. A regular set() cannot be stored this way as that would allow you to mutate the constant stored with the byte object.