For reference: There are aliens (or gods, depending on who you ask) living in a wormhole in space. For diplomatic reasons, Captain Benjamin Sisko, widower and newly appointed to the area, agrees to go inside the wormhole and try and contact the aliens (if they exist, and if they choose to speak to him) to give them a warning.
(He is also very angry, and very broken, and has sought help for neither.)
Starfleet trains their officers in how to conduct first contact with an alien species, and Sisko, when he is addressed by the aliens, does an admirable job of it. The aliens take on the appearance of people from his memories; he takes it in stride. They ask him in half-belligerent, half-frightened tones why he is here, damaging their existence; he does his best to apologize, to explain that he didn't know his shuttlecraft's systems could damage the wormhole, but that he'll fix that.
And then they ask him how he couldn't have known, and bit by bit Sisko realizes: these aliens exist with no concept of linear time. They have no basis for understanding the nature of a decision made in ignorance.
And there's Sisko, having to explain to gods what it is to be mortal.
Sisko would, after leaving the wormhole, successful in his warning, be hailed as a major religious figure in the area-- essentially a prophet (as humans use the term), someone who is able to communicate with the gods. And this is true, because he does manage to explain linear existence to these non-linear beings-- we as the audience get to see it happening, and it's amazing to watch.
But the real clincher in why he was able to finally connect with the aliens was not really the successful communication of the nature of time. It was the realization, on both parts, that humans can understand what it is to be outside of time-- because Sisko, for all that he says humans exist at a fixed point, always moving from the known to the unknown, is living perpetually in the moment his wife died.
Sisko teaches the aliens how to understand linear time, and how they too can experience it. The aliens teach Sisko how to understand that humans (and, by extension, other linear beings) can choose to live in an all-encompassing Now.
This is both a hell of a demonstration of why communication toward mutual understanding is important, but is also a thesis statement for the series as a whole.
DS9 starts with the Federation stepping in to help bolster an alien society that has only just gotten out of a multi-year genocidal occupation, setting up shop in the oppressor's own abandoned space station. As the series progresses, we see over and over that a commonality between all our different cultures and species is this haunting cognitive dissonance: time is linear for us, progressing forward forever into the unknown, taking us farther and farther from our past -- but we also, simultaneously, exist in eddies of time, both by choice and by circumstance, and we are tormented by the need to both dismiss the idea (since we are linear, we don't exist in the past, we exist now) and accept it (because our past doesn't just inform our now, but is often, in the case of trauma, something that is viscerally happening to us over and over).
The show is successful with this theme to greater and lesser degrees during its run. But as the OP said right at the top-- even in DS9's first episode, "that one.... hit"