"The core" means the central, most essential part of something. It can be a project's key goals, a team's heart, or an idea's main point. It also names the trunk muscles or the tough center of fruits like apples.
The best CEOs I know are teachers, and at the core of what they teach is strategy. Michael E. Porter
Individual science fiction stories may seem as trivial as ever to the blinder critics and philosophers of today - but the core of science fiction, its essence has become crucial to our salvation if we are to be saved at all. Isaac Asimov
The moment eternal - just that and no more - When ecstasy's utmost we clutch at the core While cheeks burn, arms open, eyes shut, and lips meet! Robert Browning
Only one mountain can know the core of another mountain. Frida Kahlo
Many a rose-cheeked apple is rotten at the core. Irish Proverb
Sodom apples outwardly fair, ashes at the core. Romanian Proverb