how numpy partition work

The documentation says:

Creates a copy of the array with its elements rearranged in such a way that the value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined.

In the example you give, you have selected 2th element of the sorted list (starting from zero), which is -1, and it seems to be in the right position if the array was sorted.

The docs talk of 'a sorted array'.

np.partition starts by sorting the elements in the array provided. In this case the original array is:

arr = [ 5,  4,  1,  0, -1, -3, -4,  0]

When sorted, we have:

arr_sorted = [-4 -3 -1  0  0  1  4  5]

Hence the call, np.partition(arr, kth=2), will actually have the kth as the the element in position 2 of the arr_sorted, not arr. The element is correctly picked as -1.