Aham brahmasmi is one of four mahavakyas, great statements, that later Advaita Vedanta drew one from each of the four Vedas, this one from the Brihadaranyaka Upanishad, which belongs to the tradition of the White Yajur Veda. The assignment of one statement per Veda, prajnanam brahma from the Rig Veda tradition, ayam atma brahma from the Atharva Veda tradition, tat tvam asi from the Sama Veda tradition and this one from the Yajur Veda tradition, is a later systematization, not something the Upanishads themselves present as a set of four, and it belongs to the monastic curriculum Shankara's tradition built for training renunciates, historically taught to students already advanced in Vedantic study rather than offered as an opening teaching. That restricted setting has mostly dissolved in the last century, and the phrase is now printed in general audience books on Vedanta without the course of study that traditionally prepared a listener to hear it correctly.
The difficulty for translation and for teaching alike is that the plain English, I am Brahman, invites exactly the misunderstanding Advaita commentators spend the most effort blocking, that the empirical, individual I, the ego with its name, memory and history, is claiming to be God. Shankara's commentarial tradition insists the aham in question is not that empirical self at all but the witnessing awareness underlying it, identified with Brahman only once the empirical self has been analysed away as a limited, changing thing the statement is not actually about. Several modern translators prefer glosses like consciousness is Brahman over the more literal I am Brahman precisely to head off the egotistical misreading, at the cost of losing the first person grammar the Sanskrit insists on.