Imagine lighting a candle. The candle emits a flash of light that travels in all directions,  forming a bubble that grows.  This bubble is in 3 dimensions and surrounds us completely. If we are inside this bubble, it is impossible to get out of it because to do so we would have to exceed the speed of light.

What Is Light Cone?

Imagine that we only perceive a 2D slice of space. The bubble forms a circle that grows all around us. If we decompose the situation image by image,  and if we stack the images one after the other, we can construct a diagram in which the bubble of light, which grows as time passes, forms a cone. This cone widens from the past to the future, and inside of it, we trace a trajectory through time. The sides of the cone are tilted at 45° because for any given amount of time, light always travels a set distance. For example, in one year, the light will always travel a  distance of  “one light-year” through space.
This type of object is called a light cone.

As time passes, the cone expands at the speed of light, and whatever we do, our path remains bound by it, it’s impossible to escape it. In relativity, these light cones are essential to understanding the structure of the universe. In particular, they restrict cause-and-effect relationships.  

To understand, imagine an event that occurs far from Earth, such as a supernova explosion. This event won’t be able to affect us until its light cone has reached Earth. Before that, no information about the explosion can reach us, since nothing can be transmitted faster than light. This explosion can only be seen and felt on  Earth as soon as we enter its light cone. “Causality,” the fact that one event can trigger another, is limited by the speed of light. More importantly, light cones allow us to understand the profound difference between the notions of “time”, and “space”

What is the difference between time and space?

Through space, we can move in any direction, turn around, or trace a path that loops back on itself...  
But through time, all objects are forced to move in the same direction.  

In time, it is impossible to turn back, we always move from the past to the future.

Light cones allow us to  clearly see this difference:  

Through space, we are free to choose any direction, but through time, the successive light cones force us to always move forwards. We cannot turn around because we are bound to remain within these lightcones.

This property allows us to define rather rigorously what we call “time”.

What Is Time?

In relativity, time is simply the direction in which the light cones are oriented. It is the direction along which we cannot turn back. This is the direction towards which all allowed trajectories point,  and in which our future necessarily lies.  

What Is Space?

Space on the other hand is the set of all other directions, perpendicular to time. In an area where the universe is empty, with no gravity, its structure, space-time, is straight.

Time and space form a symmetric, rectilinear grid,  and the light cones are all aligned in the same direction. We can thus define "time" globally:  in the diagram shown below, time goes from left to right.
But imagine now that the universe contains a  very massive body, for instance, the Earth. If we drop an apple, the apple will gradually fall downwards, deflected by the gravity of the planet. However, gravity affects not only matter, but also light. If the apple emits bubbles of light over time, it will also be drawn downwards. Close to a massive body, the light cones are no longer aligned with each other: they curve more and more, bent by gravity. Near a massive body, the direction of the light cones curves... and in other words, "time" is bent towards the center of the planet. If the apple falls, although it was motionless at first, it is because its future points downwards.

Mass distorts the geometry of the universe, and space and time become relative, their orientation depending on where we are, this is “general relativity”. The more massive a body,  the more it bends space-time. But imagine a massive object that is very compact. Such a body would generate a curvature so strong that below a certain altitude, all light cones would be completely oriented downwards. If we were to light a candle in this place, all light rays, whatever their direction, would be destined to fall towards the center… this is what we call a black hole.

What Is A Black hole?

A black hole is a spherical region of the universe, a sort of bubble, in which the curvature of space-time drives all objects towards the center. If we consider a 2D slice of space, the black hole manifests as a circle, which stays static and traces a cylinder through space-time. The boundary of the Blackhole is called the “Horizon”.  Above the horizon, some light rays can escape,  but below the horizon, all light is captured. In a black hole, lightcones force the path of any object downwards…  "Time" itself points towards the center of the black hole.

Why Time And Space Swap Into A Black hole?

To understand what a black hole really is, it is  wise to consider two different points of view: 

Imagine an astronaut who falls into the black hole, and a distant observer, stationed at a great distance.
For the distant observer, gravity is feeble,  and in his vicinity the grid of space-time is flat. For him, time flows from left to right. The horizon of the black hole seems motionless,  as it traces a straight line from the past to the future.

But let's now take the perspective of the falling astronaut. As he gets closer to the horizon,  “time” and “space” curve more and more, bent by the presence of the Blackhole. When he finally reaches the horizon of the black hole,  the astronaut does not realize it, but, at this point, time and space are tilted at 45°. For the astronaut, the horizon is not a  horizontal line from the past to the future, it’s a diagonal which rises at 45°…  exactly like the surface of a light cone.

While the distant observer sees the Blackhole  as stationary, for the astronaut at the horizon,  
time and space are tilted, such that the Blackhole behaves like a light cone, which explains why it is impossible to escape.

When he crosses the horizon, the notions of time and space seem swapped around compared to the outside: time is now pointing downwards  - which, before, was a direction through space - the horizon of the black hole is no longer a place in ​​space, but a moment in our past and the center of the Blackhole is no longer a point, but an event in our future, a destiny we cannot avoid.

Below the horizon, all objects inevitably fall, because it is in thE direction that their future lies. When a massive star collapses in on itself, it emits one last flash of light, the last bubble that tries to grow, but within a  curved space-time, bent by the mass of the star, such that the bubble seems static from the outside. A black hole has formed. It is a light cone...  rendered motionless by the curvature of space-time.

If we straighten back the diagram, we recover a global direction of time, for flowing from left to right.
In this straightened diagram, we see explicitly that the horizon of the Blackhole forms a light cone, emerging from the collapsing star, and from the inside of which it is impossible to escape.  

Once below the horizon, we are forced to hit the center of the black hole - a place where the curvature becomes so intense that our models no longer work. The center of the black hole is an event… in the future.

Finally, if we compactify thE diagram, we get a “Penrose diagram”, in which the black hole's outside  
and inside form two distinct regions. As soon as we cross the horizon, the rest of the universe is behind us, in our past. We won’t ever be able to access it again. Our only possible future is to fall…  all the way to the singularity.