From the perspective of any galaxy, most other galaxies are moving away from it, "outward". But some galaxies are close enough to form clusters that are gravitationally bound, which can cause them to orbit each other or merge.

We can say the visible universe is expanding outwards, because we see light from more and more distant things as the universe ages. But the actual (not just visible) universe may be infinitely large, we don't know what's beyond the range we can see (limited by the speed of light, unless we discover something radically new about physics we can never see farther). So if you look at the universe from a holistic point of view, not just from our perspective which makes us the center of the universe, expansion may not really be the best way to think about it. It's more like the size of the empty parts is increasing relative to the size of the not-empty parts.