In Saivite traditions of Hinduism, the term is used as part of the compound "Maheshvara" ("great lord") as a name for Siva. In Mahayana Buddhism it is used as part of the compound "Avalokiteśvara" ("lord who hears the cries of the world"), the name of a bodhisattva revered for his compassion. When referring to Divine as female, particularly in Shaktism, the feminine Īśvarī is sometimes used.
Schools of thought
Ishvara is a transcendent and immanent entity best described in the last chapter of the Shukla Yajur Veda Samhita, known as the Ishavasya Upanishad. It states ishavasyam idam sarvam which means whatever there is in this world is covered and filled with Ishvara. Ishvara not only creates the world, but then also enters into everything there is:
He created all this, whatever is here. Having created it, into it, indeed, he entered. Having entered it, he became both the actual and the beyond, the defined and the undefined, both the founded and the unfounded, the intelligent and the unintelligent, the true and the untrue. (Taittiriya Upanishad 2.6.1)
Advaitism holds that when human beings think of Brahman, the Supreme Cosmic Spirit is projected upon the limited, finite human mind and appears as Ishvara. Therefore, the mind projects human attributes, such as personality, motherhood, and fatherhood on the Supreme Being. An interesting metaphor is that when the "reflection" of the Cosmic Spirit falls upon the mirror of Maya (Māyā; the principle of illusion, which binds the mind), it appears as the Supreme Lord. God (as in Brahman) is not thought to have such attributes in the true sense. However it may be helpful to project such attributes onto God.
Vishishta Advaita Vedanta
In Vishishtadvaita, Ishvara is the Supreme Cosmic Spirit who maintains complete control over the Universe and all the sentient beings, which together also form the pan-organistic body of Ishvara. The triad of Ishvara along with the universe and the sentient beings is Brahman, which signifies the completeness of existence. Ishvara is Para Brahman endowed with innumerable auspicious qualities (Kalyana Gunas). Ishvara is perfect, omniscient, omnipresent, incorporeal, independent, creator of the world, its active ruler and also the eventual destroyer. He is causeless, eternal and unchangeable — and is yet the material and the efficient cause of the world. He is both immanent (like whiteness in milk) and transcendent (like a watch-maker independent of a watch). He is the subject of worship. He is the basis of morality and giver of the fruits of one's Karma. He rules the world with His Māyā — His divine power.
According to the Dvaita school, Ishvara possesses all the qualities seen in Vishishtadvaita. Ishvara is the efficient and material cause of the universe and the sentient beings and yet exists independently. Thus, Dvaitism does not separate Ishvara and Brahman, and does not believe that the highest form of Brahman is attributeless, or that Ishvara is incorporeal. Instead, Ishvara is the highest form of truth and worship of God involves belief in God as an infinite and yet personal and loving being.
Ishvara is simultaneously "one with and different from His creation". In this sense Vaishnava theology is not pantheistic as in no way does it deny the separate existence of God (Vishnu) in His own personal form. However, at the same time, creation (or what is termed in Vaishnava theology as the 'cosmic manifestation') is never separated from God. He always exercises supreme control over his creation. Sometimes directly, but most of the time indirectly through his different potencies or energies (Prakrti).
(I particularly like the last paragraph above, that says the supreme exists both within and outside creation and that "he" often exercises power through his "different potencies or energies. Thus it suggests (to me) that humans may contact these potencies or energies (angels? spirit guides? divinities? the "lesser" entities on the ladder of celestial essences?) rather than the ultimate reality, which perhaps is and abstract reality beyond personal communication. Hinduism is a vast and complex subject--I like to discover small bits that offer a taste of this great philosophy. Only scholars can untangle the many systems of thought. But sometimes even a glimpse can offer a great deal if it is assimilated into the mind/energy body--as, say, through a mantra, say, or an image. We do not have to be scholars in order to experience God, in whatever form ultimate essence arrives.)
(Sorry about the strange margins--somehow, this happened when I copied the above selections.)