In plain words
The eyes are able to see colours. The ears are able to hear sounds, good and bad. The tongue is able to taste flavours. The nose enjoys fragrances. In this way the working of the five elements, turned outward in daily life, goes on carrying out their own several duties. This Ātma experiences not as an individual but with the whole. That is, because this Ātma is bound up with the universe, they gave the outward-facing Ātma in this jāgrat state the name Viśva. That is, the form of the universe is itself the form of the Ātma. Viśvam is the form of Viṣṇu. That is why we must hold what is called Hṛṣīkeśa-sevanam to be most needful. This very thing, in the spirit of Bhakti, is hṛṣīkeśa-sevanaṃ bhaktir ucyate. So in the jāgrat state the Ātma takes on a form that pervades the universe.
The second is the svapna state. In it the Ātma is turned inward. In sleep itself a man goes on dreaming dreams. But in this svapna state the organs of action do not do their own work at all. Only the inner senses stay alert in it. In it only the mind and the intellect go on doing their own work. It forgets the form of the whole and moves very alertly in the form of the individual. Though ten people sleep in one room, each one's dream is his own; there is no link at all between one and another. So in the svapna state it experiences individuality alone, and there is no room at all to experience the whole. Because in this svapna state it is wholly of the form of radiance, they have called the Ātma in the svapna state Taijasa.
Next, suṣupti. Su means good. Supti means sleep. Deep sleep itself is called suṣupti. In this deep sleep the subtle senses simply do not work at all. The mind too lies dissolved in the Ātma. So it has no link at all with these senses. Neither the organs of action nor the organs of knowledge have any link with it at all. So, because at the level of suṣupti the Ātma is joined with prajñā, here it came by the name Prājña.
Next, turīya. Turīya means the fourth place; that is its meaning. In it the jīva lies merged in God. There the state of the jīva experiences the joining in oneness. But when we look at it with the body-minded outlook, it is darkness. When we look at it with the Ātma-minded outlook, it is simply complete absorption. The first is a distortion. The second is a forgetting.