Different meanings of brackets in Python

In addition to Maltysen's answer and for future readers: you can define the () and [] operators in a class, by defining the methods:

• __call__(self[, args...]) for ()
• __getitem__(self, key) for []

An example is numpy.mgrid[...]. In this way you can define it on your custom-made objects for any purpose you like.

Square brackets: []

Lists and indexing/lookup/slicing

• Lists: [], [1, 2, 3], [i**2 for i in range(5)]
• Indexing: 'abc'[0] → 'a'
• Lookup: {0: 10}[0] → 10
• Slicing: 'abc'[:2] → 'ab'

Parentheses: () (AKA "round brackets")

Tuples, order of operations, generator expressions, function calls and other syntax.

• Tuples: (), (1, 2, 3)
  • Although tuples can be created without parentheses: t = 1, 2 → (1, 2)
• Order of operations: (n-1)**2
• Generator expressions: (i**2 for i in range(5))
• Function or method calls: print(), int(), range(5), '1 2'.split(' ')
  • with a generator expression: sum(i**2 for i in range(5))

Curly braces: {}

Dictionaries and sets, as well as in string formatting

• Dicts: {}, {0: 10}, {i: i**2 for i in range(5)}
• Sets: {0}, {i**2 for i in range(5)}
  • Except the empty set: set()
• In string formatting to indicate replacement fields:
  • F-strings: f'{foobar}'
  • Format strings: '{}'.format(foobar)

Regular expressions

All of these brackets are also used in regex. Basically, [] are used for character classes, () for grouping, and {} for repetition. For details, see The Regular Expressions FAQ.

Angle brackets: <>

Used when representing certain objects like functions, classes, and class instances if the class doesn't override __repr__(), for example:

>>> print
<built-in function print>
>>> zip
<class 'zip'>
>>> zip()
<zip object at 0x7f95df5a7340>

(Note that these aren't proper Unicode angle brackets, like ⟨⟩, but repurposed less-than and greater-than signs.)

() parentheses are used for order of operations, or order of evaluation, and are referred to as tuples. [] brackets are used for lists. List contents can be changed, unlike tuple content. {} are used to define a dictionary in a "list" called a literal.