Basically, the topology on Minkowski Space-Time it’s a "3-dimensional photograph" of the Universe which continuously changes trough the time. To better explain this concept we can rely on the words of Strashimir G. Popvassilev, who is a member of the Bulgarian Academy of Science...

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The Earth, the Sun, the stars and all the matter in the space - the Universe - move and change continuously. It is hard to imagine the Universe at a particular moment: it would look like a 3-dimensional photograph with all the stars and planets fixed.

Let us imagine we have a perfect camera which can click at any particular moment. There is another difficulty: if we click from the Earth to the Sun now, we fix the Sun as it was more than 8 minutes ago - the time it takes the Sunshine (the Sun has shone 8 minutes ago) to cross 149 598 900 km space between the Sun and Earth at speed of 300 000 km/sec.

So, let us now imagine the Earth, the Sun, the stars and planets and even all the particles have their cameras, and each camera fixes only the nearest picture. Let us imagine all the cameras can click simultaneously - now we click from the Earth toward the Earth, from the Sun toward the Sun, and so on, and arrange all the photographs together forming one photograph which fixes everything as it is now. At any particular moment in the time (in the past, now, and in the future) we repeat such simultaneous clicks and what we obtain is the movie called The Minkowski Space-Time, or the 3-dimensional photograph of the Universe which continuously changes trough the time.

The concept of simultaneous clicks of all the cameras rely on the existence of a clock within each camera and depend on how all the clocks can be synchronized. Einstein's theory of Special Relativity grows out from the principle that nothing moves faster than light, in particular the best (the fastest) way for synchronizing clocks is by using light signals.

The first Einstein's principle states that all the physical laws are the same in all inertial frames of reference, and the second Einstein's principle states that the speed of light is a constant which does not even depend on the speed of its source
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Therefore, Einstein unified space and time with his theory of relativity; Minkowsky invented a triangle to graphically illustrate equality and invariance of the space-time theory.

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Source(s):
http://at.yorku.ca/t/a/i/c/28.htm

http://www.quantonics.com/Einstein_Minkowski_Space_Time_Diagram.html

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