Gravitational instability is an instability in the dynamics of a system stemming from characteristics of the gravitational field. A simple example is an object residing at a L1 point between two co-orbiting bodies, which, if for any reason moves slightly closer to one or the other body, will fall away from the point.
Secular gravitational instability (secular GI) refers to such an instability that occurs over a long period of time, i.e., from situations in orbits where overall gravitational force is periodically different, leading to slight changes that grow over time.
The term gravitational instability is common in discussion of the dynamics of matter spread out, such as dark matter, clouds, or disks, referring to situations where any occurrence of extra density receives positive feedback. It is a consideration in the formation of anything that gathers matter, i.e., galaxy clusters, galaxies, stars, and planets. It can be prevented by sufficient relative velocity, or by a force counteracting gravity, such as pressure. The gravitational instability model, referring to protoplanetary disks, is of interest regarding planet formation of gas giants.