: is the delimiter of the slice syntax to 'slice out' sub-parts in sequences , [start:end]

[1:5] is equivalent to "from 1 to 5" (5 not included)
[1:] is equivalent to "1 to end"
[len(a):] is equivalent to "from length of a to end"

Watch https://youtu.be/tKTZoB2Vjuk?t=41m40s at around 40:00 he starts explaining that.

Works with tuples and strings, too.

As suggested from numpy's documentation about indexing you can use the slice built-in function and tuple concatenation to create variable indexes.

In fact the : in the subscript is simply the literal notation for a slice literal.

In particular : is equivalent to slice(None) (which, itself, is equivalent to slice(None, None, None) where the arguments are start, stop and step).

For example:

a[(0,) * N + (slice(None),)]

is equivalent to:

a[0, 0, ..., 0, :]   # with N zeros

The : notation for slices can only be used directly inside a subscript. For example this fails:

In [10]: a[(0,0,:)]
  File "<ipython-input-10-f41b33bd742f>", line 1
    a[(0,0,:)]
           ^
SyntaxError: invalid syntax

To allow extracting a slice from an array of arbitrary dimensions you can write a simple function such as:

def make_index(num_dimension, slice_pos):
    zeros = [0] * num_dimension
    zeros[slice_pos] = slice(None)
    return tuple(zeros)

And use it as in:

In [3]: a = np.array(range(24)).reshape((2, 3, 4))

In [4]: a[make_index(3, 2)]
Out[4]: array([0, 1, 2, 3])

In [5]: a[make_index(3, 1)]
Out[5]: array([0, 4, 8])

In [6]: a[make_index(3, 0)]
Out[6]: array([ 0, 12])

You can generalize make_index to do any kind of things. The important thing to remember is that it should, in the end, return a tuple containing either integers or slices.