I Need the explaination of The image of formation of black hole

The vertical dimension represents time, the horizontal dimension space. If you take a horizontal cross-section of the diagram it shows the position of the surface of the star and of the event horizon at a given time--you can see that the radius of the star steadily shrinks and the radius of the event horizon grows from the point in space and time labeled "O", until the event horizon reaches a fixed radius at the moment the collapsing star is fully inside it. The representation of the singularity as a wavy line is just a visual convention, don't take it literally.

 

Yes, it's a standard space-time diagram, which puts time on the vertical axis. (I'm not quite sure where this convention came from).

The horizontal axis represents the radial spatial coordinate using a spherical coordinate system (r, theta, phi). To fit the diagram on a 2d page, theta and phi are omitted (the problem is symmetrical in theta and phi anyway).

The vertical lines are drawn at the instant the body collapses to form a black hole. They represent light cones at that point. They illustrate that the path of light has a constant spatial coordinate, hence the light is "trapped" by the gravity / geometry of the black hole when a certain point in the collapse process is reached.

Until the object collapses sufficiently, the light is not trapped. The event horizon forms and the light is trapped only when the object is contained within its Schwarzschild radius.