The shape attribute for numpy arrays returns the dimensions of the array. If Y has n rows and m columns, then Y.shape is (n,m). So Y.shape[0] is n.

In [46]: Y = np.arange(12).reshape(3,4)

In [47]: Y
Out[47]: 
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])

In [48]: Y.shape
Out[48]: (3, 4)

In [49]: Y.shape[0]
Out[49]: 3

This is quite common in computer vision the first dimension being the number of examples, the second and third provide the data of the examples. In the case of computer vision for example it is quite common to have a set of n images with shape (x,y). In this case your training set will be of the shape (n,x,y). The fourth dimension in your data is the number of channels (3, or RGB in this case).

In your dataset the height and the width of each image is the same and thus the size of the image can be retrieved merely by the third line: num_px = train_set_x_orig.shape[1]

x is a 2D array, which can also be looked upon as an array of 1D arrays, having 10 rows and 1024 columns. x[0] is the first 1D sub-array which has 1024 elements (there are 10 such 1D sub-arrays in x), and x[0].shape gives the shape of that sub-array, which happens to be a 1-tuple - (1024, ).

On the other hand, x.shape is a 2-tuple which represents the shape of x, which in this case is (10, 1024). x.shape[0] gives the first element in that tuple, which is 10.

Here's a demo with some smaller numbers, which should hopefully be easier to understand.

x = np.arange(36).reshape(-1, 9)
x

array([[ 0,  1,  2,  3,  4,  5,  6,  7,  8],
       [ 9, 10, 11, 12, 13, 14, 15, 16, 17],
       [18, 19, 20, 21, 22, 23, 24, 25, 26],
       [27, 28, 29, 30, 31, 32, 33, 34, 35]])

x[0]
array([0, 1, 2, 3, 4, 5, 6, 7, 8])

x[0].shape
(9,)

x.shape
(4, 9)

x.shape[0]
4