The expansion of the universe is the increase in distance between gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion, so it does not mean that the universe expands "into" anything or that space exists "outside" it.

To any observer in the universe, it appears that all but the nearest galaxies (which are bound to each other by gravity) move away at speeds that are proportional to their distance from the observer, on average.

While objects cannot move faster than light, this limitation applies only with respect to local reference frames and does not limit the recession rates of cosmologically distant objects.