I'm a 90s kid. Born and raised in that ever transitional decade, I grew up watching lots of science-fiction. Star Trek: The Next Generation (TNG) was ongoing when I was born, and among the series that followed were Star Trek: Deep Space Nine, Star Trek: Voyager, and Star Trek: Enterprise.
Until the start of Deep Space Nine (DS9), the format of the Star Trek series had been fairly straight-forward and predictable. For the most part, episodic encounters with alien races in the context of space and exploration. Sure, there were recurring villains with story-arcs, but the context of the series remained the same - a mixed-species crew exploring the galaxy. The was the case in the original Star Trek (TOS) and TNG. It was essentially the same in Enterprise and Voyager (in the case of Voyager, it was still exploring the galaxy but with the added goal of returning home after being stranded in the Delta Quadrant).
This is where Deep Space Nine broke the mold. But first, let us set the stage.
In previous series, it was established that modern human space exploration took place under the banner of the Federation, aka the United Federation of Planets. A consortium of alien races with a storied history of wars and ongoing tensions. In TOS, TNG, DS9, Voyager, and Enterprise, the federation plays a central role - mission command*, and this is a key point.
[*With the exception of Star Trek: Enterprise, a prequel series which lays the ground work for the formation of the Federation.]
In every other series, the Federation gave an explicit mission of active exploration. In DS9, we see the first intended mission of static occupation. No exploring, an explicit "stay here." As opposed to an weekly "meet-the-alien" episode, we have a series where we will explore the nuanced politics and repercussions of space exploration.
In DS9, we meet newly widowed Commander Benjamin Sisko, who is given the boring task of occupying, Deep Space Nine, a space station, to maintain the peace between the Cardassians and the Bajorans.
If you haven't seen or know nothing of the series, Sisko is the first Black commanding officer and lead character.
Sisko is also the only officer in command to start off not as Captain, but as Commander. We later see him promoted to Captain.
Going back to the topic of diversity among the cast. We have Jadzia Dax, the first female second-in-command. Don't forget Miles O'Brien, the first character to canonically serve on multiple ships (in later seasons, we have also get Worf).
Kira Nerys is fantastic. As a former Bajoran freedom fighter, she politicizes everything, and as a result, we expound on the background of the Federation and explore the topic of space politics. Deep Space Nine being a space station that essentially functions like a port of call, there are a bevy of interactions between alien races, another opportunity to explore race politics in space! The background context and realities that are spoken of in passing on other series play out in DS9.
If the groundbreaking storylines stopped there, DS9 would still be the greatest series, but they don't. Even though we have an explicit static mission objective, the discovery of a wormhole to the Gamma Quadrant, quickly escalates what might have otherwise been an action-less peacekeeping mission into an actively militaristic operation. So much, much more nuanced space politics.
To add more fantastic-ness, Benjamin Sisko finds himself at the center of the local religion as the much-prophesied Prophet! Reluctant at first to see himself in this light, over a number of seasons, he accepts this role from a political and religious standpoint!
Not only do we get time travel, we learn more about the Eugenics War and the early days of the federation. Even though it starts off passive, it is anything but with a giant alien race war playing out over seasons.
I won't give away anything more, but if you doubt my words and my argument, go watch DS9; then say something.
So to summarize, Deep Space Nine is great because of:
Diversity! Representation matters!!
The expansion of the Star Trek Universe
There are a number of reasons why DS9 is outstandingly the best television series in the Star Trek universe and if you have more or disagree, leave a comment!