The Core Conflict is the conflict that the other conflicts build off of. However, let’s take Star Wars for example (Just like everyone ever). The core conflict is say ‘Will the Empire Succeed in destroying the rebels?” (perhaps not the deepest analysis, but whatever). This question drives the entire movie. Then you have your surface conflicts that are a part of the core conflict such as “Will R2 escape with the data?” and “Will they rescue princess Leia?” Each of which are great conflicts, but not core one.
Core conflict can also refer to what you get when you drill down into exactly what you mean by your central conflict. For example, “Will they blow up the death star?” is one way to state the core conflict, but it might be less useful in helping you come up with ideas for your surface conflicts. It’s perhaps a bit too concrete. Whereas something like “Can good overcome evil?” Suffers the same problem, but is too abstract. Something in the middle, such as ‘Will the Empire Succeed in destroying the rebels?” (Still just spitballing rather than really deep analysis. here.) Might better help you understand how to develop your surface conflicts.
The Core Conflict can also refer to a character’s conflict as well. What it is that they have to overcome internally to succeed. For example, Han has to overcome his worldliness to commit to something beyond himself.
How you state it can change your perspective on scenes. For example, if you were to state the Core Conflict of Star Wars as “Will Luke overcome his worldliness to put trust in a higher power (the force)?” That gives you a very different reading of Han Solo than does something like “Can friendship overcome greed?”
I do slightly worry that I’m perhaps sounding a bit wishy-washy here, the reason for that is because Core Conflict isn’t a binary right/wrong but a way to bring things into focus like a camera lens. You can dial it from utterly concrete to completely abstract to get something that is useful to you and what you want to accomplish.
The core conflict is a tool, and a very useful one because your core conflict should also be driving your surface conflicts. Part of what went wrong in the Phantom Menace (I love that movie and the Podracing, but whatever) is that the Podracing scene took up a significant part of the movie, but was more peripherally to the core conflict than it’s screen time implied. Because the core conflict was out of focus, it wasn’t as good as it could have been. This can be contrasted with the escape from the Death Star in A New Hope scenes where the core conflict is fully in focus as they are directly confronting the force of antagonism (the empire) and having a mixed success. (They escape with the princess at the loss of the mentor.) Because the core conflict is in focus, the action scenes are more effective.