A hegemonising swarm is a group of self-replicating entities with no purpose beyond expanding, multiplying, and turning every piece of matter they encounter into more of themselves. A more typical word used for these outside of the Culture series is "Von Neumann probe", or even grey goo for the small-scale terrestrial-bound equivalent.
The argument has been made that all civilizations are, at their core, hegemonising swarms to one degree or another, the Culture in particular given its ethos of staying as it is while making other civilizations more like itself. Because of this, The Culture does not deal with hegemonising swarms as pests or existential threats in need of destruction, but as another legitimate, if misguided, form of intelligent life only to be destroyed as a last resort.