What is the universe expanding through?

[D.B. Cooper]

I've always heard that the universe is forever expanding, but through what? Space? What is the universe "inside of"? It boggles the mind.

[jrs90]

Infinite vacuum
and this too i guess:

Contrary to popular understanding, outer space is not completely empty (i.e. a perfect vacuum), but contains a low density of particles, predominantly hydrogen plasma, as well as electromagnetic radiation and neutrinos. Hypothetically, it also contains dark matter and dark energy.
WIKI

[Juvenal]

The Universe is everything (by definition), including space (and time). So when we say the Universe is expanding, we mean space itself is expanding and that the constituents of the Universe are drawing further apart.

It is not known if the Universe is finite or infinite. We can only (theoretically) observe a bubble up to 46 billion light years in all directions (the distance light can have travelled since the Universe first became transparent, magnified by the expansion of space during that time). What astronomers observe is that in general everything we see is moving away from us, its speed proportional to distance (this fact being derived from the phenomenon of Red Shift).

The conclusion is that in the past everything was closer together, and that before 13.7 billion years ago, everything we now see was in the same place and the Universe was infinitely dense.

The Universe includes all of space, there isn't any more space outside the Universe for it to expand into. There (probably) isn't an edge of the Universe. It is either infinite, or finite and closed in on itself like the three-dimensional equivalent of the surface of a balloon.

[Holger Danske]

Then we have the Multiverse theory...