Meaning
Īśvara (Sanskrit: ईश्वर) — from īś (to rule, to be master of) — means the Supreme Ruler, the One who has complete sovereignty over all existence. In Viśiṣṭādvaita, Īśvara is unambiguously identified as Śrīman Nārāyaṇa — not any other deity — as the ultimate and highest reality.
Īśvara's Unique Status
While chit (souls) and achit (matter) are both real and eternal, Īśvara alone is sva-tantra (absolutely independent), sarva-vyāpaka (all-pervading), sarva-niyantā (controller of all), and sarva-śeṣī (the ultimate end for whom all exists). Chit and achit are paratantra — entirely dependent on and existing for Īśvara.
The Antaryāmi Doctrine
Iśvara's relationship to chit and achit is that of the antaryāmi — the Inner Controller who dwells within every soul and every particle of matter, directing them from within, yet remaining untouched by their limitations. This doctrine, drawn from the Antaryāmi Brāhmaṇa of the Bṛhadāraṇyaka Upaniṣad, is a cornerstone of Viśiṣṭādvaita.
Śrī as Inseparable
In Śrī Vaiṣṇavism, Īśvara is never conceived without Śrī (Pirāṭṭi/Mahālakṣmī), who is eternally inseparable from Him. She is His śakti and His purushakāra (intercessor) for all souls seeking refuge. The compound 'Śrīman Nārāyaṇa' encodes this inseparability.