Many and perhaps all galaxies seem to contain supermassive black holes of about $10^7 M_\odot$ at their centres. Determining their origins is of great astrophysical interest.
In what I understand to be the currently-favoured theory of "hierarchical merger", the supermassive black holes get larger over time via repeated mergers between smaller holes, during for example galactic mergers. This requires a natural mechanism dissipating orbital energy and angular momentum between the holes such that they will generically merge in much less than a Hubble time.
When the holes are very far apart (much further than a parsec) such a mechanism exists in the form of gas drag (EDIT: the actual mechanism here is dynamical friction; thanks Chris White for pointing this out). And when they are very close the gravitational radiation reaction becomes important. But at distances of about a parsec the holes don't seem to be driven together, and according to current theory should never merge. Thus the "final parsec problem": how do we get the holes close enough together for a merger to happen?
However as far as I'm aware there isn't actually any evidence that the black holes ever do merge. A large swarm of small black holes about a parsec apart would be equally compatible with observation. Or else some process other than hierarchical merger could account for the holes. So it seems this "problem" has more to do with the careers of gravitational wave scientists than with any actual difficulty in astrophysics. Or am I being unfair?