Brahman is described as ekamevadvitiyam, one only without a second. The word monism, as said in my comment, is often used interchangeably in common parlance with non-dualism (or advaita (not two)), but strictly speaking it is referred to as non-dualism, not monism.
The Chandogya Upanishad (VI. ii. 1.) says (Swami Gambhirananda translator):
'O good looking one, in the beginning this was Existence alone, One only, without a second...'
And Sankara's commentary on this (Swami Gambhirananda translator):
By the words 'One only' is meant that there was nothing else coming under the catergory of Its product. By the words 'without a second' this is meant: As in the case of pot, etc. some other efficient causes like potters and others, who are different from earth etc. into pot etc. are seen, similarily (here) also there arises the possibility of having some other second thing which is different from Existence, and yet is a cause associated with Existence. This is being denied by the phase, 'without a second (advitiyam)'. So, 'without a second' means that It (Existence) has no second thing different from Itself.
In his commentary on verse II. 33. of Gaudapada's Karika of the Mandukya Upanishad, Swami Nikhilananda says:
Vedanta describes Brahman, or Atman, as non-dual or as one and without a second--not simply as one.
And further (The Upanishads V1, p 34-35), Swami Nikhilananda says:
Brahman is "one and without a second"--ekamevadvitiyam, The second part of the phrase ("without a second"), qualifying the first ("one"), is important for what it means is that Brahman is not one in the same sense that the sun or the moon is one, or in the sense that the God of the monotheist is one. In such a case there is a perceiver of the oneness--which implies duality. When the non-duality of Brahman is completely realized, there is absolutely no consciousness of subject and object; the distinction between perceiver and perceived is annihilated and they become one.
So although used often in common parlance to mean the 'non-dual', 'monism' only implies 'one' and does not imply the 'without a second'. Advaita means not two. Scriptures say that Brahman is beyond words, beyond description, beyond all perception; and the only thing that can be said of It is neti, neti - not this, not this. As such 'not two' or 'non-dual' or advaita is a better description of the philosophy.