Not to be confused with Brahma, the Hindu god of creation/manifestation, Brahman literally means "great" or "the Big." The implication is Brahman is bigger than the biggest; that which goes beyond all experience itself and accommodates all things (brahmanatva brahman). And yet, we ought not think of Brahman in physical size but in that which is not limited by time or space because Brahman is that which is beyond all objects—including time and space.
Brahman cannot be described in words because Brahman is not an object of experience. How is one to describe something that is attributeless, actionless and not available to the senses? Instead, scripture, a kind of "word mirror," uses signs that point to Brahman as the Self—the eternal subject.
Ultimately, Brahman can only be described using a process of negation (neti-neti) or by using indicators/pointers (lakshanas). One classic example of the latter is the analogy of the clay and the pot, where it is shown that the essence of the pot is clay and that the pot itself is just name and form. Similarly, the essence of who/what we are is Brahman (the clay), while the body-mind (the pot) is just an object known by Brahman (pure awareness). When the pot is broken it is no longer a pot, and yet the clay (the truth of the pot) remains.
Nevertheless, it's not a question of whether or not Brahman can be known. Brahman can be known because Brahman is self-evident. Brahman is the "I am" when I say "I am a man," "I am a son," "I am an employee," etc. We needn't be taught that I exist, because "I" as the Self, is the one thing that can never be denied.
In his translation and commentary on the Upanishads, Swami Nikhilananda writes:
As Brahman is the essence of Being, so It is the essence of Consciousness or Light. Brahman needs no other light to illumine Itself. It is self-luminous. 'It is pure; It is the Light of lights; It is That which they know who know the Self.' All material objects, such as trees, rivers, houses, forests, are illumined by the sun; but the light that illumines the sun is the light of Brahman. 'The sun does not shine there, nor the moon and the stars, nor these lightnings, not to speak of this fire. When He shines, everything shines after Him; by His light everything is lighted.'
Referring to Brahman as "Him" shows it has religious overtones. Brahman is often categorized as both God with qualities (Saguna Brahman) and God without qualities (Nirguna Brahman). The former is God as creator, sustainer and destroyer of the universe (Brahman plus maya), while the latter is God as pure, attributeless awareness—the Self. However, there is only one absolute and that is Nirguna Brahman. Knowledge of Nirguna Brahman is the culmination of God knowledge and considered the highest form of devotion.
The three traditional epithets for Brahman are existence, consciousness and bliss. These are not separate attributes of Brahman but instead synonyms, such that we say Brahman is existence-consciousness-bliss, or in Sanskrit, sat-chit-ananda. Sat is existence absolute, that is, the "I am" or the is-ness of our everyday contact with objects. Chit is consciousness absolute and is also sometimes translated as "pure knowledge "or "knowledge as such" (but shouldn't be confused with the mind or the workings of the mind). Lastly, ananda is bliss absolute. "Bliss" in this case equates to perfect satisfaction as a result of the absence of any limitation. "Limitlessness” is sometimes used instead of bliss in order to remove the confusion with Brahman being some kind of state of ecstasy (Brahman is not a state or a feeling). So, when Brahman is described as bliss, it’s really showing that its nature is absolute freedom. All objects are of the nature to bind, only formless Brahman is of the nature to be limitless.