The word Tathagata is one of the common epithets of Buddha. In Japanese, Nyorai.
Tatha is sometimes rendered into English as the neologism "Thusness" which renders the word into a sort of English without making the meaning particularly clear and leaving a nice ambiguity.
If you want a rather secular, materialistic interpretation of Buddhism, then you can take thusness as meaning "things as they are" and say that the tathagata is one who sees things as they actually are - however you think that that is.
However, in the context of Indian religion this probably does not work unless by "things as they actually are" you mean how they are in the eyes of God. The word Tatha derives from "tat" which in common speech means "that". At first sight this look innocuous enough. However, the key slogan of traditional Indian religion is "Tat tvam asi" which means "Thou art That" where That means God, Brahma.
The basic meaning of this slogan is that the fundamental part of a person is a fragment of God and the purpose of religion is that all those fragments be ultimately reunited with Brahma. There can be little doubt that the Buddhist use of Tat and Tatha were framed within this kind of perspective but with a shift of meaning.
In Pali, we also say "Namo Tassa". Here Tassa is also a derivative of the same root. This phrase means "I take refuge in That One", That One being the Buddha. All of these phrases attribute a divine dimension to Buddha. Modern people do not like this and try to argue their way around it. They prefer to emphasise that Siddhartha Gotama was a human being. This is due to the intense humanism of our age. However, it is a misreading of Buddhism. Buddhism does not think of divinity in the same way as we are used to in monotheistic religions, but nonetheless, it is the spiritual presence of Buddha that is considered important - more important than God, in fact.
What impressed his followers in Asian history was not how human he was but precisely the other aspect - how divine, or more-than-divine, he seemed. Clearly he had something about him that was not common, not ordinary, not just like everybody else, and that "something" is what is called Tat or Tatha - "That" or "Thatness". It is That in which Buddhists take refuge.
Now let us look at the other half of the word Tathagata. "Gata" means gone. If we read the whole word this way then it means that the Buddha has gone to the transcendent domain, the spiritual world, the sphere that Buddhists are forbidden to speculate about but which clearly is intended to be taken as being wonderful, marvellous and consummate, the goal of the spiritual life.
So if Buddha is the "One Gone to That Domain" then our task is to exert ourselves to do what he did and follow. This is the self-power approach to Buddhism. the rousing slogan of this philosophy is "The Buddhas do but point the way; thou must walk the path alone; strive on with diligence."
However, Tathagata can also be scanned as Tatha-agata. Agata means come. Now Buddha is the one who has come from the transcendent realm. In this view, Buddha has come to help and save us. This is the other-power perspective on Buddhism. When Buddha comes to us in this way, our part is to receive Him, be grateful, open ourselves, be humble and receptive. The Japanese term Nyorai definitely means Tatha-agata, since "rai" in Japanese means "come". So Japanese Buddhism, not just in the Pureland Schools, is shot through with an other-power perspective. The slogan here is, perhaps, the haiku of Honen Shonin that reads: "The moon shines into every hamlet in the land, but only those who gaze upon it carry it in their hearts."
Of course, although particular schools of Buddhism may have different emphases, some mix of self-power and other-power is always apparent in practice. They are like the yang and yin of Buddhism. Tathagata comes to us, Tathagata walks ahead, sometimes glancing back. Tathagata urges us forward along the narrow path. there are many images, each picking up a different aspect of how we are helped. Different people need different things and the same person has different needs at different stages. The Buddhas are not limited by our concepts. their compassion extends limitlessly.