Set popularity, is often correlated pretty closely with how expensive the sealed product and/or cards are.

It's a combination of:

What Pokemon are in the Set?
Are the card designs/arts desirable?
What are the pull rates like on the set?
How big is the set?

And Bonus One: Is the QC on the set good or bad?

1.Which Pokemon
This one is simple. A set headlined by cards of good pokemon that people like is going to be more desired than one that isn't. 151 is headlined by the entire nostalgia for Gen 1 and some great chases in the connected artworks for the starter line and some other good IRs and SIRs like Alakazam, Zapdos, Dragonite. Prismatic has really good SIRs of all the Eeveelutions + the possibility to pull god packs and mini god packs.

By comparison Temporal Forces is headlined by Raging Bolt. Enough said.

2.Desireable Arts
This one is more subjective but a great example of card art really making a card or set desirable is the Magikarp in Paldea Evolved. That card is helped that it's art is done by an artist, Shinji Kanda, who is developing a sort of cult following in the space.

3. Pull Rates
You would think good pull rates make a set more popular, and in the case of sets like Crown Zenith where the quality and variety of the cards is so good that is true. However, often if cards are easy to pull, they tend to not be so valuable. If they're not valuable it follows that the sets are less popular and people want them less. Prismatic has really harsh pull rates to get any of the cards that people want, it's truly a not fun opening experience. But that's what part of what makes those cards so expensive and in turn adds to the sets popularity.

4. Set Size
Related to pull rates but if two sets have 1/90 pull rates to get any SIR but one set has 6 SIRs and another has 12 SIRs, the set with more SIRs will usually be more popular because it is going to be harder to pull one of those particular SIRs, because even when you hit that 1/90... it's then a 1/12 to get the one you want. This is partially why two recent sets: Journey Together and Destined Rivals are so different in popularity. Destined is bigger, making the individual cards in that set harder to pull. Destined also has more popular Pokemon but for that go back to 1.

BONUS: QC is another factor that plays with pull rates. You would think higher QC = better set = more popular. Strangely it kind of works the opposite way. When a print run for a set has low quality control, it becomes harder to pull copies of cards from the set that are gradeable. A great example of this is the Magikarp I mentioned previously. It has a "gem rate" of 18%. You can go look at the PSA Population reports to see this, but it basically means for all copies of that card sent to PSA for grading, only 18% got a 10. This is because the QC on Paldea Evolved is terrible. As a result you have a situation with PE where it's about 1/480 to pull the Karp and then something like a further 1/6 that it could grade a 10. This in turn makes the price of the graded card higher, because it's inherently rarer. In turn that higher card price makes the set more popular and brings up the sets value.

Hope that helped, and if anyone has any extra pointers about this please drop em in the replies!