I'm reading a book about string theory, and it tells me in the future it could be possible to detect existence of other bubble universes through cosmic background radiation. Is this true? What could we potentially see?
The book is referring to this paper. As far as I can tell (which is not very far! :-) the maths is valid, but whether the maths describes anything that happens in the real world is another question.
If you're reading books in this area you've probably heard of inflation, i.e. the idea that the universe expanded exponentially soon after the Big Bang. When the universe stops inflating we get the slowly expanding universe that we see around us today.
There is a theory called Eternal Inflation in which different bits of the inflating universe stop inflating at different times. This gives many areas that look like our universe today, but those areas are separated in the sense that you'd need to be able to travel faster than the speed of light to get from one of these areas to another. Because of this separation these areas are generally known as bubble universes. Arguably this is a misnomer, since the bubble universes are really just different areas of a single inflating universe, but it's only terminology so I can't get too wound up about it.
Anyhow, it's possible that two bubble universes might be close enough that they could touch each other. The idea behind the paper is that the interaction between the two bubble universes would change the cosmic microwave background (CMB) and this change would be detectable. Various searches of the CMB have been done looking for evidence of such a collision, but so far nothing has been found.
If you want to find out more about this Google for "universe collision CMB" or something like that. One of the hits will be this blog, which I recommend as a good description of the idea.