The current explanation is that "space" is continuously created in the intergalactic void, "pushing" the galaxies apart. From what i understood ( i am also ignorant ), the current rate at which "space" is created is expressed by the Hubble's constant 67.15 ± 1.2 km/s/Mpc ): for every million parsecs of distance from the observer, the rate of expansion increases by about 67 kilometers per second, which means that the distance between 2 points that are 1 megaparsec apart grows with 67km every second; between 2 points that are 2 megaparsecs apart with 134km/s, and so on so the relative speed between 2 points that are 5000 Mpc apart would be 335000 km/s which is more than the speed of light. In fact, two objects at this distance would not move, but 335000km worth of "extra space" would be "created" between them every second.
However in the last week there was an article depicting the shape of the universe, and it is hard for me to understand how it got to look like this : http://ifreepress.com/wp-content/uploads/2014/09/laniakea.png
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