The word tryadhīśvara means "proprietor of the three worlds." There are three worlds of which Kṛṣṇa is the supreme proprietor. This is explained in Bhagavad-gītā:

bhoktāraṁ yajña-tapasāṁ
sarva-loka-maheśvaram
suhṛdaṁ sarva-bhūtānāṁ
jñātvā māṁ śāntim ṛcchati

"The sages, knowing Me as the ultimate purpose of all sacrifices and austerities, the Supreme Lord of all planets and demigods and the benefactor and well-wisher of all living entities, attain peace from the pangs of material miseries." (Bg. 5.29)

The word sarva-loka means "all three worlds," and the word maheśvara means "the supreme proprietor." Kṛṣṇa is the proprietor of both material and spiritual worlds. The spiritual world is divided into two portions-Goloka Vṛndāvana and the Vaikuṇṭhas. The material world is a combination of universes unlimited in number.