Schwarzschild Radius and Event Horizon

An imaginary projectile launched from the Sun's surface would require a velocity of 618 km/s to escape the Sun's gravitational field.

Now, suppose the Sun's radius is reduced by half, keeping its mass constant. Then its escape velocity would increase to 873 km/s. If the radius is decreased further, eventually to 2.9 km, the escape velocity will equal the speed of light.

Recall that the escape velocity of a projectile depends on the mass and radius of the object from which it is launched.

In general, the radius at which any mass has an escape velocity equal to the speed of light is called the Schwarzschild radius. Therefore, Schwarzschild radius equals twice the product of gravitational constant and the object's mass divided by the square of light's speed.

Any spherical non-rotating object having a radius smaller than its Schwarzschild radius is called a black hole. 

The spherical surface surrounding the black hole, at Schwarzschild radius,  is known as the event horizon, inside which the escape velocity is greater than the speed of light.