Space itself is expanding, like a stretching rubber sheet. Or a balloon's skin as it is inflated. It isn't expanding into anything. If you like, it creates the space as it goes. There's no edge or center. Every point in the universe is rushing away from every other point. On the subatomic right up to the human scale electromagnetism and the strong nucleic force hold objects and people together while the negligible (at such scales) expansion occurs underneath. On larger scales like star systems, galaxies and galactic clusters gravity holds things together while the expanding space between them whooshes past unnoticed. But on scales larger than that, the intergalactic distances between clusters, there is so much distance that the space expanding between them makes everything rush away from everything else, and this is quite noticeable. A Doppler shift occurs to the light, lengthening the wavelength and changing the colours of distance objects as they appear to us. This is called the redshift. On the most distant of objects, part of that redshift may be due not only to the Doppler effect, but also the the actual expansion of space itself stretching out the wavelength as the light mores through it, something that could only be noticeable after billions of years of travel. Which such light has had.
Expansion appears to be speeding up. Sooner or later the furthest galaxies will be too distant to make out with any telescope, their light redshifted into the invisible portions of the spectrum, and eventually not even able to reach us as the space expands faster than the light can travel across it. Had humanity evolved during such a period in the universe's future, it would be quite impossible to learn anything at all about the nature and origin of the universe. All the evidence would have gone and left us behind.
If there is anything beyond the universe it cannot be thought of to have a position in relation to the universe. Coordinates only work inside the universe, where there are dimensions that the coordinates can correspond to.
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