Aham Brahmasmi is one of the four mahavakyas of Brihadaranyaka Upanishad. Everything is supposed to be obtainable by the knowledge of Brahman. But, if the self is to be realized by the knowledge of Brahman, in what way did Brahman understand Himself?
Even before the creation of this universe, Brahman knew as ever Himself as aham brahma asmi. What do these three words mean?
The meaning of Aham Brahmasmi is explained in Narayan Stuti and Madhvacharya explains it as adumbrated in the said Shruti: aham – aheyam – undiscardable; brahma – absolutely perfect; asmi – ever aware of self existence. By these three adjectives, Brahman comprehended Himself, and it does not just mean I am Brahman.
If aham (I) is taken as a pronoun in the first person singular and asmi (am) is taken as singular verb then the object atmanam (himself) would be redundant. Therefore, Madhvacharya affirms that the explanation offered above is the most appropriate, i.e. He understood Himself (tadatmanamatmavat) as aham brahma asmi.
In several Vedic passages quoted in Bhashya, the word aham appears. In all those cases aham means “inner controller” and “undiscardable”.
In Shruti passage, tadyoham sosau, aham brahmasmi where the word aham is involved, one should not take aham as jivatman, but identified with paramatman. This is not a proven proposition. This confusion is clarified by the statement in Chandogya Upanishad, a tattvamasi – (Thou art not that).
Source – Encyclopedia of Hinduism Volume I page 102 - IHRF