The eternal inflation model says that there's an infinite number of universes, with new universes constantly popping into existence and expanding outwards. Every so often, these new universes might collide. Our universe has four "bruises" possibly caused by these collisions.
We've already found possible evidence of a universe before the Big Bang in the cosmic microwave background, so why not other universes? This particular theory comes out of a model known as eternal inflation, which suggests universes are constantly popping up and expanding throughout the vast, unimaginably infinite cosmos.
We know our universe underwent its own inflationary period just after the Big Bang, carving out our own little sphere of the cosmos. The idea is that, as universes pop into existence around each other and start to expand, the space between them also expands at a slightly faster rate, keeping the universes forever separate. But it isn't actually required that the space between expands faster than the universe, and that opens up the possibility of entire universes colliding into each other, the victims of runaway expansion.
Such a collision would release massive bursts of energy into both universes. As long as the collision occurred while our own universe was still inflating, then there would be telltale artifacts left behind in the cosmic microwave background. Basically, the collision would cause inflation to proceed unevenly in that part of the universe - if it lasted longer than elsewhere, that part of the CMB would be cooler, while it would be warmer if the collision caused inflation to end sooner.
Astronomers have now found at least four possible "bruises" left behind by other universes colliding into our own. These four massive cold spots in the CMB can't really be explained if ours is the only universe, as there's nothing we know of in our universe that could create these spots.
Still, the absence of alternative theories isn't by itself proof of other universes. However, there actually are ways to confirm the theory, such as the orientation of the photons making up that portion of the CMB. The European Space Agency's Planck satellite should be able to pick up on the polarization of the photons and possibly prove or disprove the theory. Its first maps are due in 2012.
Even if we can't find conclusive proof for most of the candidates, confirming even one spot as an artifact of a collision with another universe would be a massively important finding, providing crucial support for theories that rely on the existence of a multiverse. It might also completely destroy our sense of perspective once and for all, to find out we really are just in one of an infinite array of universes.