Brahman is that which is permanent in things that change. It is without name and form, which two are the characteristic natures of the world of appearance, and is essentially existence-absolute. Existence can never change, never perish, though things in which also it is, perish. Hence existence is the nature of Reality and is different from the things of form and name.
According to a commentary of Shri Madhavacharya on Srimad Bhagwat Gita Chapter 4 Verse 8
The Supreme Lord Krishna is also designated as Brahman which means eternal in time and dynamic in creativity and is the all pervading luminosity of His effulgence. It is not inert or passive. The word Brahman which is derived from the root brh means to grow, to burst forth which infers constant, continuous creativity, perpetually manifesting. That which is dynamic and creative cannot remain static and passive.
Here is an another source from Indian Philosophy
The word ‘brahman’ is derived from the root ‘bṛṃhati’ meaning ‘great’ which again is not limited by any qualification of time, space, or quality, that is, which is unlimitedly great. We have to accept this meaning because there is nothing to signify any limitation of any kind (saṃkocakābhāvāt). The Brahman is different from all that is animate (cetana) and inanimate (acetana). There are two kinds of energy: that which is the representative of the material power or energy (jaḍa-śakti), which transforms itself in the form of the material universe under the direction or instrumentality of the Brahman; and there is also the energy as consciousness (cicchakti), and this consciousness energy, as we find it in animate beings, is also controlled by the Brahman