1. You have entities, which may just be identifiers (maybe a u64 used as an index elsewhere) or some more complex object.

2. You have components, which are the real "meat and potatoes" of things. These are the properties or traits of an entity, the specifics depend on your application. For a video game or physics simulator it might be velocity and position vectors.

3. Each entity is associated with 0 or more components.

4. These associations are dynamic.

5. You have systems which operate on some subset of entities based on some constraints. A simple constraint might be "all entities with position and velocity components". Objects lacking those would not be important to a physics system.

In effect, with ECS you create in-memory, hopefully efficient, relational databases of system state. The association with different components allows for dynamically giving entities properties. The systems determine the evolution of the state by changing components, associating entities with components, and disassociating entities from components.

The technical details on how to do this efficiently can get interesting.

Compared to more typical OO (exaggerated for effect), instead of constructing a class which has a bunch of properties (say implements some combination of interfaces) and manually mixing and matching like:

  Wizard: Player
  FlyingWizard: Wizard, Flying
  FlameproofWizard: Wizard, Flameproof
  FlyingFlameproofWizard: Wizard, Flameproof, Flying

So your party enters the third floor of a wooden structure and your Wizard (a component associated with an entity) casts "Fly" and "Protection from Elements" on himself. These associate the entity with the Flying and Flameproof components (and potentially others). Now when fireball is cast and the wizard is in the affected area, he'll be ignored (by virtue of being Flameproof) while everything around him catches fire, and when the wooden floor burns away the physics engine will leave him floating rather than falling like his poor non-flying, currently on fire Fighter compatriot.