They compare arrays (matrices) element-wise and return True/False for each element in the arrays. Check the following example:
>>> import numpy as np
>>> a=np.array([[11,12,13],[14,15,16]])
>>> b=np.array([[12,12,11],[18,9,16]])
>>> a
array([[11, 12, 13],
[14, 15, 16]])
>>> b
array([[12, 12, 11],
[18, 9, 16]])
>>> np.equal(a,b)
array([[False, True, False],
[False, False, True]])
>>> np.not_equal(a,b)
array([[ True, False, True],
[ True, True, False]])