DS9's Children of Time is a touching story of family, perseverance, growth, and sacrifice. Let's explore the core Star Trek principles it presents below.
Moral Dilemma
Perhaps no theme is more central to Star Trek than a moral dilemma. Children of Time presents a challenging one - should the crew of the Defiant avoid the anomaly and return home to their families, resulting in the 8,000 people in the settlement being erased from existence, or should they purposefully try to recreate the accident and intentionally strand themselves here (and sacrifice Kira's life)?
There's another subtle twist to the moral dilemma too - should Yedrin Dax attempt to deceive his ancestors, robbing them of the choice to return home but ensuring the survival of the colony? Ultimately he decides to do this and it almost works, until Jadzia figures out the deception.
Character Growth
Odo
No character has more obvious, visible growth than Odo. From the improved shape-shifting abilities to a stronger command of his emotions, this Odo is able to connect with Kira on a level that present day Odo simply cannot. His openness reveals to Kira how Odo has always felt about her and ignites the possibility of the romance that later develops between them as the series progresses.
Worf
Worf's legacy and his commentment to Klingon principles are alive and strong, preserved and passed down through future Sons of Mogh. That he was able to creat such a strong following that lasts for generations is a testament to his principles and discipline.
He also helps his descendents grow beyond his original teachings by showing them an honorable challenge rather than a cowardly way to spend their final hours:
Descendent: "You said there was an enemy for us to fight."
Worf: "They are attempting to plant their fields before the sun sets. Time is their enemy. We should help them defeat it."
O'Brien
O'Brien strongly resisting any attempts to get close to the colonists, wishing desperately to return to this family on DS9. Yet even he, after being forced by Sisko to interact, realizes how precious they are and desperately declares "we can't leave these people!".
Plot Twist
Ultimately, Captain Sisko makes the decision that they will return home; they will not attempt to save the colony. In a touching final goodbye, they agree to help the colonists plant their fields in their annual planting ritual.
As it progresses, even stubborn O'Brien comes around. In a complete reversal, and at Kira's insistence, they plot a course for the anomaly and plan to strand themselves there and sacrifice Kira. At the last second, the Defiant pulls away from the anomaly and they escape, with no trace of the colony remaining on the planet's surface. We later learn that the older Odo had sabatoged the ship to ensure they would not get stranded and thus Kira would live.
It's powerful to watch the characters wrestle with this dilemma and evolve their position on the situation. Both the Defiant's crew and the viewers are left saddened that these warm, joyful colonists have ceased to exist.
Parting Message
In classic Star Trek fashion, Children of Time ends on a positive note with Captain Sisko declaring that "they existed. As long as we remember them, they always will".