When talking about galaxy clusters there is the frequently used phrase "gravitationally bound", f.e. we are gravitationally bound to our neighbor galaxy the Andromeda Galaxy. But how is this statement mathematically defined since gravitation has an infinite reach, we (the Milkyway) have a tiny gravitational influence on any other galaxy in the universe.
It means the total energy (kinetic + gravitational potential) is negative. This assumes the convention that gravitational potential energy approaches zero as the distance tends to infinity, and is negative for all finite distances.
So if I imagine an airless planet the same size and mass as the Earth, A ball that is moving at 10 km/s (away from the planet, at the planet's surface) won't have enough kinetic energy to keep moving away from the planet forever. It will move away and slow down as kinetic energy is converted to potential and eventually halt and fall back. Its total energy is negative, and it is gravitationally bound to the planet. On the other hand, a ball moving at 12 km/s will continue to move away forever, gravity will slow it down but never completely stop it. The ball moving at 12km/s has positive total energy.
You can do the same thing, but on a much larger scale with galaxies. The Milky-way Andromeda system has negative total energy, and so is gravitationally bound. But more distant galaxies have positive (or very close to zero) total energy.