I am posting this to help in keeping recurring mentions of this issue from derailing other threads. The astronomers who coined the expression know among themselves what they mean by it, as is the case with lots of other jargon. Some newbies here may not know, so here are my thoughts.
A large planet clears its immediate neighborhood of all but transient small stuff by the following:
1. Gravitationally eject an interloper that otherwise could occupy a similar orbit that repeatedly comes close.
2. Collide with the interloper, adding to its own mass in the process.
3. Gravitationally shepherd small bodies into stable Trojan orbits, so they stay an average of 60 degrees ahead of or behind the planet, never coming close. Jupiter is the best known example.
4. Gravitationally shepherd small bodies into stable 2:3 resonance orbits as Neptune does with Pluto and many smaller KBOs. They may cross Neptune's orbit but the dynamics are such that these bodies stay widely separated from Neptune, thus leaving its immediate surroundings clear. Other resonance patterns are possible.
We could figuratively say that the planet throws its weight around and forcibly maintains plenty of elbow room. Bodies that are not massive enough to do this in their territory are classified as dwarf planets or various lesser objects.
These neighborhoods will never be totally clear because perturbations deflect asteroids and comets into them in small quantities. The orbits of these interlopers, if closed, are unstable and short-lived on a cosmic time scale.