Paramhansas are those who can discriminate right from wrong, real from fake, and truth from untruth.
This requires a lot of discriminative power, which evolves slowly as you go deeper on the spiritual path, imparting to you a clear vision.
So, a hansa (swan), a mythical figure in scriptures, is known to distinguish between milk and water, which to us appear as a single entity.
Sansar is that milk, where the pure water of Godliness (energy, urja, awareness) is already hidden in it, but remains invisible to our sansaric vision.
The physical form of the Sansar is that milk, Maya, and it hides the pure and subtle water of Godliness.
When your inner journey deepens, the ability to discriminate also sharpens.
One who has sharpened their power of discrimination to the max is called Paramhansa (the highest swan).
In that state, one does not run away from Sansar, but stays where he is and sees it with a different vision – the inner eye of awareness (which in reality is the only eye there is).