I took a Gross Anatomy class long ago. We did not just have to learn every muscle, tendon, and bone in the hand and foot because our Prof was more interested in how they function as systems, smoothly in unison.
One of the first things he taught, before we began cutting up human bodies, was that we higher apes were designed to be quadripeds, not bipeds. The adaptation to bipedalism came with great advantages but with disadvantages too. Like joint arthritis.
The thing is that to stay erect much of the day, instead of momentarily like other apes, we need extra anti-gravity systems - including balance. That's "the core." Well, many people sit most of the day and that's not so good.
So let's accept that all of our body needs difficult movement to remain functional, but the core is the core. Foundational.
What is core? It is primarily the "posterior chain", from glutes to upper back. Secondarily, to counterbalance that, the abdominal groups of muscles.
While there are plenty of posterior chain exercises, the mighty mighty deadlift done right is the best single thing for the entire core, posterior and abdominals. Some might argue that sit-ups, crunches, and the like are useful but I view them as accessory core exercises.
This gal's technique is not quite right - knees way too close and back too arched, but I give her credit for being there: