Lets say that a dot in reality is represented by a dot in your picture. Your eyes and brain in combination will form an opinion about how well the picture shows the dot, and if it is in focus or not. The shape and the size of the dot is the deciding factor.
Here is the thing: Your evaluation is not binary! In other words, you don’t make a “flip a switch” assessment, rather you accept some minor deviations in the way the dot is shown in your image. Sometimes the dot is spot on (he-he) and other times it is a bit oval or a bit larger that the real thing.
The interval in which you accept the dot to be sharp is known as the circle of confusion. Don’t ask me how this term came about, but the point is that accept small variations and still think of it as sharp.
It is the circle of confusion that gives us depth of field! The fact that minor variations in how the dot in reality is represented in the picture, gives us some wiggle room before and after the focus plane and this is exactly the DoF. Without a circle of confusion there would be no DoF!