Python interning:

>>> a = "hello"
>>> b = "hello"
>>> c = "world"
>>> id(a)
4299882336
>>> id(b)
4299882336
>>> id(c)
4299882384

Short strings tend to get interned automatically, explaining why a is b == True. See here for more.

Depending on the context here it could different things:

indexing/slicing with Ellipsis

I think it's not implemented for any python class but it should represent an arbitary number of data structure nestings (as much needed). So for example: a[..., 1] should return all the second elements of the innermost nested structure:

>>> import numpy as np
>>> a = np.arange(27).reshape(3,3,3)  # 3dimensional array
>>> a[..., 1]  # this returns a slice through the array in the third dimension
array([[ 1,  4,  7],
       [10, 13, 16],
       [19, 22, 25]])
>>> a[0, ...]  # This returns a slice through the first dimension
array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])

and to check for this ... you compare it to an Ellipsis (this is a singleton so recommended is using is:

>>> ... is Ellipsis
True
>>> Ellipsis in [...]
True
# Another (more or less) equivalent alternative to the previous line:
>>> any(i is Ellipsis for i in [1, ..., 2]) 
True

Recursive Datastructures

The other case in which you see an [...] in your output is if you have the sequence inside the sequence itself. Here it stands for an infinite deeply nested sequence (that's not printable). For example:

>>> alist = ['a', 'b', 'c']
>>> alist[0] = alist
>>> alist
[[...], 'b', 'c']

# Infinite deeply nested so you can use as many leading [0] as you want
>>> alist[0][1] 
'b'
>>> alist[0][0][0][0][0][1] 
'b'
>>> alist[0][0][0][0][0][0][0][0][0][0][0][0][0][0][0][1] 
'b'

You can even replace it several times:

>>> alist[2] = alist
>>> alist
[[...], 'b', [...]]
>>> alist[1] = alist
>>> alist
[[...], [...], [...]]

To test if you have any such recursion in your output you need to check if the data-structure itself is also one of the elements:

>>> alist in alist
True
>>> any(i is alist for i in alist)
True

Another way to get a more meaningful output is using pprint.pprint:

>>> import pprint
>>> pprint.pprint(alist)  # Assuming you only replaced the first element:
[<Recursion on list with id=1628861250120>, 'b', 'c']

Python's standard library has gc module containing garbage collector API. One of the function you possible want to have is

gc.get_objects()

This function returns list of all objects currently tracked by garbage collector. The next step is to analyze it.

If you know the object you want to track you can use sys module's getrefcount function:

>>> x = object()
>>> sys.getrefcount(x)
2
>>> y = x
>>> sys.getrefcount(x)
3

As Chris Lutz explains, this is defined by the __repr__ method in your class.

From the documentation of repr():

For many types, this function makes an attempt to return a string that would yield an object with the same value when passed to eval(), otherwise the representation is a string enclosed in angle brackets that contains the name of the type of the object together with additional information often including the name and address of the object. A class can control what this function returns for its instances by defining a __repr__() method.

Given the following class Test:

class Test:
    def __init__(self, a, b):
        self.a = a
        self.b = b

    def __repr__(self):
        return f"<Test a:{self.a} b:{self.b}>"

    def __str__(self):
        return f"From str method of Test: a is {self.a}, b is {self.b}"

..it will act the following way in the Python shell:

>>> t = Test(123, 456)
>>> t
<Test a:123 b:456>
>>> print(repr(t))
<Test a:123 b:456>
>>> print(t)
From str method of Test: a is 123, b is 456
>>> print(str(t))
From str method of Test: a is 123, b is 456

If no __str__ method is defined, print(t) (or print(str(t))) will use the result of __repr__ instead

If no __repr__ method is defined then the default is used, which is roughly equivalent to:

def __repr__(self):
    cls = self.__class__
    return f"<{cls.__module_}.{cls.__qualname__} object at {id(self)}>"

Try Finding objects' names, it prints all names that reference a given object.