The criterion to satisfy for providing the new shape is that 'The new shape should be compatible with the original shape'

numpy allow us to give one of new shape parameter as -1 (eg: (2,-1) or (-1,3) but not (-1, -1)). It simply means that it is an unknown dimension and we want numpy to figure it out. And numpy will figure this by looking at the 'length of the array and remaining dimensions' and making sure it satisfies the above mentioned criteria

Now see the example.

z = np.array([[1, 2, 3, 4],
         [5, 6, 7, 8],
         [9, 10, 11, 12]])
z.shape
(3, 4)

Now trying to reshape with (-1) . Result new shape is (12,) and is compatible with original shape (3,4)

z.reshape(-1)
array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12])

Now trying to reshape with (-1, 1) . We have provided column as 1 but rows as unknown . So we get result new shape as (12, 1).again compatible with original shape(3,4)

z.reshape(-1,1)
array([[ 1],
   [ 2],
   [ 3],
   [ 4],
   [ 5],
   [ 6],
   [ 7],
   [ 8],
   [ 9],
   [10],
   [11],
   [12]])

The above is consistent with numpy advice/error message, to use reshape(-1,1) for a single feature; i.e. single column

Reshape your data using array.reshape(-1, 1) if your data has a single feature

New shape as (-1, 2). row unknown, column 2. we get result new shape as (6, 2)

z.reshape(-1, 2)
array([[ 1,  2],
   [ 3,  4],
   [ 5,  6],
   [ 7,  8],
   [ 9, 10],
   [11, 12]])

Now trying to keep column as unknown. New shape as (1,-1). i.e, row is 1, column unknown. we get result new shape as (1, 12)

z.reshape(1,-1)
array([[ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12]])

The above is consistent with numpy advice/error message, to use reshape(1,-1) for a single sample; i.e. single row

Reshape your data using array.reshape(1, -1) if it contains a single sample

New shape (2, -1). Row 2, column unknown. we get result new shape as (2,6)

z.reshape(2, -1)
array([[ 1,  2,  3,  4,  5,  6],
   [ 7,  8,  9, 10, 11, 12]])

New shape as (3, -1). Row 3, column unknown. we get result new shape as (3,4)

z.reshape(3, -1)
array([[ 1,  2,  3,  4],
   [ 5,  6,  7,  8],
   [ 9, 10, 11, 12]])

And finally, if we try to provide both dimension as unknown i.e new shape as (-1,-1). It will throw an error

z.reshape(-1, -1)
ValueError: can only specify one unknown dimension

in numpy, creating a matrix of 100X100 items is like this:

import numpy as np
x = np.ndarray((100, 100))
x.shape  # outputs: (100, 100)

numpy internally stores all these 10000 items in an array of 10000 items regardless of the shape of this object, this allows us to change the shape of this array into any dimensions as long as the number of items on the array does not change

for example, reshaping our object to 10X1000 is ok as we keep the 10000 items:

x = x.reshape(10, 1000)

reshaping to 10X2000 wont work as we does not have enough items on the list

x.reshape(10, 2000)
ValueError: total size of new array must be unchanged

so back to the -1 question, what it does is the notation for unknown dimension, meaning: let numpy fill the missing dimension with the correct value so my array remain with the same number of items.

so this:

x = x.reshape(10, 1000)

is equivalent to this:

x = x.reshape(10, -1) 

internally what numpy does is just calculating 10000 / 10 to get the missing dimension.

-1 can even be on the start of the array or in the middle.

the above two examples are equivalent to this:

x = x.reshape(-1, 1000)

if we will try to mark two dimensions as unknown, numpy will raise an exception as it cannot know what we are meaning as there are more than one way to reshape the array.

x = x.reshape(-1, -1)
ValueError: can only specify one unknown dimension

Your question is not entirely clear, so I'm guessing the -1 part is what troubles you.

From the documantaion:

The new shape should be compatible with the original shape. If an integer, then the result will be a 1-D array of that length. One shape dimension can be -1. In this case, the value is inferred from the length of the array and remaining dimensions.

The whole line meaning is this (breaking it down for simplicity):

1. points = np.array([x, y]) -> create a 2 X 5 np.array consisting of x,y
2. .T -> transpose
3. .reshape(-1, 1, 2) -> reshape it, in this case to a 5X1X2 array (as can seen by the output of points.shape [(5L, 1L, 2L)])