Here's my simple explanation. Making a game with object hierarchies, you might do the equivalent of this:

    monster = {}              // create an entity
    monster.hp = 10           // give it properties
    monster.pos = [0,0,0]

Using ECS, you instead do the equivalent of this:

    currID = 1                // ECS init
    hpData = {}
    posData = {}

    id = currID++             // create an entity
    hpData[id] = 10           // give it properties
    posData[id] = [0,0,0]

Obviously neither version is really implemented that way, but hopefully it shows the key insight - instead of storing properties on the object they describe, you store them in tables full of like data, keyed by the ID of the object they describe.