Famously Plato banned poets from his Republic; in one dialogue he had Socrates pokes a little fun at Ion, a rhapsodist - a singer of songs - for being unable to explain his gift for a rousing emotion in his audience.
Ion is actually a little afraid of Socrates questions; he wants to escape, perhaps he is thinking: stop thinking, Socrates and listen; listen to my song, and allow yourself to be carried away; then you'll understand - that just by listening naturally, one understands with no explanation ever being articulated or even found neccessary.
But Socrates persists, for he is a persistent man; eventually he explains it for Ion: he says Ion, when he sings - and especially when he sings well; he is not himself, he is transported out of himself (ekstasis - out+stand) and by virtue of his art, he is able to do the same for his audience.
They, the audience, when listening to his song, are reliving or anticipating a passion - the same passion; so they are brought to a kind of unity where not:
'being confined by our mental and physical boundaries'
We realise we are not alone; and see each other, eye-to-eye.
This explains the first paragraph.
The second paragraph is the same, said differently and more intimately; for there is no suggestion of an audience, but only you and an artwork - perhaps a piece of music, perhaps walking into a courtyard, or a painting glanced at; or again, a book of poems, as in the answer by @Barzell.
Another example along the same lines, but in a quieter key is to glance at a painting by Vermeer, and recognise a moment of contemplation in a moment of aloneness; which Vermeer too must have felt to have chosen this moment to paint; and that fills that moment and erases the aloneness and connects artist to the viewer in a moment of recognition; some spark of spirit abolishes time and distance; and therefore brings
'a kind of elation for the lonely self'
Which even if not glanced at again, but recalled later - perhaps much later, brings back that
'experience of reassurance'
One is indeed, again, not alone.