The common lore has it that in addition to hosting 10-100 billion stars, all galaxies are also covered in a massive invisible layer of dark matter. One cannot see this dark matter, nor is its composition known. Nevertheless, one can see the effects of the dark matter indirectly by the way they alter the motions of those myriad stars.
If one imagines each galaxy to be an apricot pit, then the dark matter is the orange fruit surrounding the pit. The stars in this analogy would all be situated inside the pit. If one find a way to separate the pit from the fruit by just a little bit then one could get important information concerning the properties of this mysterious dark matter.
There are no giant humans in space to bite into the fruit. Second best, if we could ram together two massive galaxies then we just might be able to see some of the fruit separated away from the pit.
This is a challenge to do in practice, as it requires knowing that the two galaxies have high motion towards each other across the sky (motion transverse to the line of sight). This measurement is generally infeasible given that the best way to do it is to wait a long time (millions of years), and hope to see that the two objects have moved a tiny amount in that time.
By contrast, it is easy to find galaxies with high motion in the radial direction towards or away from us. This is done by measuring their relative Doppler motion (the same technique used by the police to catch people speeding on the freeway).
In some special cases, we can find examples of two massive objects moving towards each other with high transverse motion. Namely, astronomers have found two massive galaxy clusters that we think have collided. Think two American football teams comprised of apricots with helmets in a free-for-all charge.
In this case we do measure a separation of the center of the dark matter (the fruit), from the center of the stars (the pit). As a result, we are starting to learn about how dark matter acts differently from ordinary matter, although we still cannot point to the dark matter and tell which substance it actually is.