In one sentence
Brahman is the absolute ground of all existence — the single reality of which everything (including atman) is an expression.
The depth — what it actually means
In the Vedanta tradition the Gita synthesises, atman and brahman are ultimately the same. The individual self and the universal absolute are not two different things; they are the same reality known from inside and from the whole. The Upanishads put it as tat tvam asi — "that thou art." The Gita is more conservative than the Upanishads on the question of identity, but the underlying claim is the same: the deepest "I" in you is not separate from the deepest reality of the universe.
Modern application — how to use this today
You do not have to believe this metaphysically to use it. Try this experiment: in a moment of strong distress, notice that the awareness in you that knows the distress is not itself distressed. That awareness is the doorway the Gita is pointing at. You do not have to call it brahman. Just notice it is there.